Gratitude
is the inward feeling of kindness received. Thankfulness is the natural impulse
to express that feeling. Thanksgiving is the following of that impulse.
Wednesday, 24 November 2021
Lupine Publishers | Whishing You A Happy Thanksgiving Day
Lupine Publishers | Robotics in Education and Training
Lupine Publishers | Advances in Robotics & Mechanical Engineering
Introduction
In Finland, a new teacher called Elias at primary school who has endless patience for repetition and never creates a pupil feel humiliated for asking same question again and again and can even do “Gangnam Style” dance. Elias is also robot. The Artificial Intelligence language machine includes a humanoid robot at primary schools in southern city of Tampere. This robot can able to understand and speak 23 different languages and it also allows to understand student’s requirements and helps to inspire learning. It recognizes student’s skill levels and adjusts its questions accordingly and gives feedback to teachers about pupil’s possible problems. Below are some of few from many applications of robots that can be used in education, teaching and training. [1].
Teaching Robots are More
Consistent Teammates
Scholars
at U.S. Army Research Laboratory and Robotics Institute at Carnegie Mellon
University have created completely a new design to teach robots with innovative
traversal behaviors with very low human intervention. This kind of technology
allows portable platforms to navigate autonomously in various environments.
Researchers focused their initial research and development in learning robot
traversal performance with respect to robot’s visual perception of territory
and objects in the environment; robot was trained how to navigate from various
stand point in the environment while staying near the edge of the road and to
traverse covertly using buildings as cover. As per scholars, these robots were
given various mission tasks, the most appropriate learned traversal behavior
can be started during operation of the mission. This can be accomplished by
leveraging optimal control that is referred as inverse reinforcement learning,
it is a class of machine learning that looks to recover a reward function. If a
robot acts as a teammate, then multiple tasks can be achieved faster with
better precision and more situational awareness can be achieved.” was confirmed
by Wigness [2] (Figure 1).
Figure 1: Illustrates a small unmanned Clear path Husky robot, which was used by ARL researchers to develop a new technique to quickly teach robots novel traversal behaviors with minimal human oversight. Image Credit: US Army [2].
Robots Can Boosts Children’s
Education
Educational
Robots play a vital role in educating young people but may not replace human
teachers completely. As per researchers, scientist say that social robots are
demonstrating effective in teaching certain narrow subjects, for instance
vocabulary or prime numbers. This study collected in concurrence with academics
and involved a review of more than 100 published articles which have shown
robots to be effective at increasing outcomes because of their physical presence.
However, it also says that leading social robots into the school course would
face significant logistical challenges and may carry risks with some children
been seen to rely completely on the robots rather than simply using them when
they are in difficulty. Authors of study also add “Considering practical
considerations of introducing robots in education also brings ethical issues.
For example, how far do we want the education of our children to be delegated
to machines?” [3,4] (Figure 2).
Figure 2: Illustrates one of the robots used in the University of Plymouth’s Robo21c program, which aims to complement to the school curriculum by developing teachers’ skills and understanding of robotics and programming. Image Credit: University of Plymouth [4].
Programming Robots Just by
Casual Talking
Robots
are getting smarter day by day, but they still need step by step instructions
for tasks they didn’t implemented before. For example, before you tell your
household robot “make me a bowl of ramen noodles” you may have to teach it how
to do that. Since we are not all computer programmers, we would prefer to give
instructions in English just like we talk to a person. The robot may have built
in programming language with look (pan); use (pan); carry (pan, water tap);
fill up (pan, water); carry (pan, heater) and so on. In this research, this
software convert’s human sentences such as “Fill a pan with water, put it on
the heater, heat the water. When it’s in boiling state, add the noodles” in the
robot language. If you had notice you never said, “Turn on the heater.” The
robot has to be smart enough to fill in that missing step. The robot
accomplished correctly up to 64 percent of the time even when the commands were
varied, or environment was different; it was able to perform missing steps.
That was three to four times better than previous methods, the researchers
reported, but there is still room for improvement [5] (Figure 3).
Figure 3: Illustrates a computer science professor is teaching robots to understand instructions in natural language from various speakers, account for missing information, and adapt to the environment at hand. Image Credit: Image courtesy of Cornell University [5].
Robots and Kids Learn Together
The
Robotic software is based on learning by teaching. When children experience
problems in writing they may easily lose confidence and gradually lose interest
in learning process. Eventually, their complete education can be affected. When
students put themselves in the place of instructor and pass on what they know
to their peers, they can regain self-esteem and motivation. Researchers
constructed an advanced writing algorithm and implemented them on an existing
robot model. With all these algorithms, machine can draw words on demand and
then eventually improve. But to do, it uses a very vast database of handwriting
examples, which allows it to reproduce common mistakes made by young children
while learning. It can also be possible to program the robot so that it
addresses the specific difficulties of a student, for example by drawing that
is barely readable and improving its form over time. The robotic system is
still in the prototype stage that has already been used in primary school
lessons with around seventy students ranging from six to eight years old and
then individually with a six-year-old child for one hour per week over one
month [6] (Figure 4).
Figure 4: Illustrates Kids and robots learning to write together. Image Credit: Image from video courtesy of Ecole Polytechnique Fédérale de Lausanne [6].
Robotic Help for Deaf Children
Swivel
is tunable robot which is placed on a tablet or iPad. It is placed in the classroom
and turns to follow people talking. It then uploads video to a secure cloud for
streaming. This novel device was developed by University of Manchester and
their team to help assess classroom training for students on its deaf education
course. This program requires trainees to be assessed in the classroom. The
Swivl technology has been used in three locations with five students. The
footage is then uploaded to the cloud and forms part of the external,
independent assessment process. Then students were able to use the recordings
to review their own work in the classroom and imitate on their learning –
something that they cannot do on traditional placements. The team is estimating
the experiences of both the students and supervisors in order to understand how
they can improve and extend the use of the technology [7] (Figure 5).
Figure 5: Illustrates one of the trainees using the technology. Image Credit: The University of Manchester [7].
Read More Lupine Publishers Robotics Journal Articles:
Tuesday, 16 November 2021
Lupine Publishers | Robotic Farmers in Agriculture
Lupine Publishers | Advances in Robotics & Mechanical Engineering
Introduction
Revolution of Robotic
farmer is on the way, fruit picking machines are ready to roll into the fields
and will replace human workers at one point of time. A Robot Farmer is just a
one of the new technologies that will completely transform agriculture sector.
Today’s agricultural technology helps farmers to plow and spray crops. In an
improved automation and big data analytics with farming robot technology are
pointing out to big benefits. Goldman Sachs estimates precision farming – the
combination of agriculture and technology could be around $240 billion market
by 2050. As per Euro monitor intersection of robotics, artificial intelligence,
analytics and machines for precision farming is one of the top industry’s top
opportunities. In Europe, Spanish company called Agrobot has developed a
strawberry farming robot. It uses up to 24 robotic arms to pick fruit and is
capable of autonomous navigation. In England, Dogtooth Technologies are
developing its own series of autonomous robots capable of picking fruit. Dogtooth
machines are proficient enough of autonomous navigation, locating and picking
ripe fruit and grading its quality [1] (Figure 1).
Figure 1: Illustrates Harvesting CROO’s machine is headed for farms in Florida and California. Image Credit: Image courtesy of Harvest CROO Robotics [1].
Robotic Weeders
The increasing
recognition of robotic weeders for specialty crops has grown – Specialty crops
are vegetables like lettuce, broccoli, tomatoes and onions. These are not
produced in mass like corn, soybeans and wheat. The reason for robotic weeders
steams from two major issues. One is a deficiency of herbicides available for
usage in specialty crops. Another issue; as a matter of fact hand-weeding has
become more and more expensive. Without pesticides, growers have had to hire
people to hand-weed vast fields. Hand weeding is very slow and increasing
expensive, it can cost around $150-$30 per acre. That is one of the reasons
some people look to robotic weeders. The robotic weeders are programmed to
recognize a pattern and can differentiate between a plant and the soil.
Although, they currently are having trouble to differentiate between a weed and
a crop. The robotic weeders in the market cost between $120,000 and $175,000,
it is a better longterm option than expensive hand weeding. Fennimore considers
that robotic weeders are the future of weeding for specialty crops. The reason
because of higher labor costs and more incentives to grow organically with less
pesticides. European growers have been using robotic weeders for a while [2]
(Figure 2).
Figure 2: Illustrates robotic weeder is operating in a field near Santa
Maria, CA. Image Credit: Image courtesy of Steven Fennimore [2].
Harvesting Cucumbers Through Robots
In automation areas for
instance, automotive industry are not the only ones to depend on robots. In
agriculture, automation systems are surpassing strenuous manual labor. As a
project, the Fraunhofer Institute for Production Systems and Design Technology
developed and tested a dual arm robotic system for automated harvesting of
cucumbers. In Germany, cucumbers are ordained for pickles that are harvested
with the aid of “cucumber flyers” – a farm vehicles with wing like add-ons.
Many of the country’s agricultural regions subsequently face an uncertain
future; cucumber farming has already begun moving to Eastern Europe and India.
Thus, there is a pressing requirement for improved harvesting technologies to
maintain economic viability of cucumber farming in Germany. Experts developed a
dual arm robot system consisting of inexpensive light modules. This system is
used for automated cucumber farming and other agricultural applications. This
Robotic cucumber picker is cost effective, high performance and dependable.
Even in adverse weather, it is capable of first identifying ripe cucumbers and
then using its two gripper arms to gently pick and store them. This novel
method can also make it possible for to imitate human movements. Scientist want
to make sure that it does not damage crops or pull to their roots out of the
soil. This robotic cucumber harvester is as efficient as its experienced human
counterpart, who can pick as many as 13 cucumbers per minute. Cucumber farmers
and agricultural associations have expressed significant interest in the dual
arm robot [3] (Figure 3).
Figure 3: Illustrates prototype of the dual-arm robot system during the first field tests. Image Credit: Fraunhofer IPK [3].
Harvesting Broccoli using Robots
This Project was jointly
funded by BBSRC and create improvements in United Kingdom; in this 3D camera
technology was used to recognize and select whether broccoli is ready for
collecting. It is the key step towards the development of an automatic robotic
harvesting system for broccoli, which will not only considerably decrease
production costs but also decrease amount of labor cost. This project also addresses
challenges associated with recognition, deterrence and management of disease by
creating diagnostic tools for farm use and substitute to chemical pesticides.
This will allow the major producers in these industries to rapidly analyze the
existence of disease and enable earlier decision making. It is also expected
that this development of project will create long-needed substitute to use of
pesticides by mushroom and potato industries therefore ensuring future
sustainability [4] (Figure 4).
Figure 4: Illustrates the TerraSentia robot that autonomously monitors crops earned the best systems paper award at Robotics: Science and Systems, the preeminent robotics conference held in Pittsburgh. Image Credit: TERRA-MEPP Project [6].
Counting Crop Using Robots
Crop breeders run large
scale of trials comparing thousands of varieties of crops over hundreds of
acres and measure key qualities, for instance emergence of plant, height, by
hand. This task is expensive, inaccurate, time consuming and completely
inadequate; team can only measure these manually by fraction of plants in a
field. TerraSentia is a compact transportable robot weight about 24 pounds and
13 inch wide. It can capture each plant from to bottom using advanced suite of
cameras, deep learning and complex algorithms. Using a method called learning
method, experts taught TerraSentia to count corn plants with just 300 images.
It is a TERRA-MEPP research task that is low cost phenotyping robot to
recognize top performing crops. This research was controlled by the University
of Illinois in collaboration with Cornell University and Signetron with
sustenance from Advanced Research Project Agency – Energy [5,6].
Combatting Weeds by Laser Robots
Farmers who want rich
harvest and need to drive weeds so that crops can cultivate better. In organic
agriculture – herbicides are not considered as they are toxic chemicals and
only unwanted plants should be arduously weeded out. This time-consuming work are
taken care of laser robots. Computer Experts in Photogrammetry at University of
Bonn have developed a new system using advanced cameras on all terrain robot
vehicle or tractor add-on and unwanted wild weeds are automatically identified
in various crops and taken out. Scientists are moving forward for their startup
to develop the business plan for this novel technology and also working to buy
the parts required for the project to construct a prototype. At University of
Bonn, Chamber of Commerce and Industry, both founders won an award for the best
novel technology. “The aim is to contribute in achieving more sustainable
agriculture. The robot fires the leaves of unnecessary plants in the crops with
short laser pulses, which weakens in their strength” [7].
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Friday, 8 October 2021
Lupine Publishers | Editorial on Self-Healing Robots
Lupine Publishers | Advances in Robotics & Mechanical Engineering
Introduction
Scientists
at University of Colorado, Boulder had developed a first and fully re-healable
and recyclable electronic material. This novel technology functions like
properties of human skin, capable of measuring pressure, temperature and
vibration. Technically, it’s a self-healing Robot - For instance if robots are
wrapped in an electronic material that mimics as human skin; theoretically it
can also sense objects that is too hot or too cold or if more or less pressure
needs to be exerted on an object. If this material is beyond repair, then it
can be soaked in a solution that separates out the silver nanoparticles then be
fully recycled into new usable material [1] (Figure 1).
Figure 1: Illustrates self-healing material developed at University of Colorado, Boulder. Image Credit: Quartz [1].
Self-Healing Robots Breakthrough
Many
of natural organisms have the capability to heal themselves. Now, manmade
machines will be able to imitate this phenomenon. In the research Carnegie
Mellon University created a self-healing material that spontaneously heals
itself even under extreme mechanical damage. The soft composite material is
consisting of liquid metal droplets suspended in a soft elastomer. When it is
broken, the droplets rupture to form a new arrangement with adjacent droplets
and redirect electrical signals without any disruption. Circuits which are
created with conductive traces of such kind of material remain entirely and
continuously functioning when punctured, severed or material removed.
Applications for this kind of novel technology includes bio-inspired robotics,
wearable, computing human and machine interaction. Because material also
exhibits high electrical conductivity; it does not change when starched,
theoretically, it is ideal for use in power and data transmission.
“If
we have to build machines that are more compatible with the human body and
natural atmosphere, then we have to begin with new material types” was
confirmed by the author of the study [2,3] (Figure 2).
Figure 2: Illustrates a digital clock continues to run as damaged circuits instantaneously heal themselves, rerouting electrical signals without interruption. Image Credit: Nature Materials [3].
Delicate, Soft and Self-Healing Robot
A
new class of delicate and soft, electrically activated robots are capable of
imitating the expansion and contraction of natural muscles. These robots which
can be designed from a wide range of low-cost materials and are able to
self-sense and self-heal from electrical damage, representing a major advance
in soft robotics. A challenge in the field of “soft robotics” that can imitate
the versatility and performance. Nevertheless, Keplinger Research Group in the
College of Engineering and Applied Science has created a novel method of a new
class of soft robotics. This novel method of hydraulically intensified
self-healing electrostatic actuators abjure bulky, rigid pistons and motors of
conventional robots for soft structures that respond to applied voltage with
comprehensive range of motions. These soft robots can accomplish a variety of
jobs including holding subtle objects for instance, raspberry and a raw egg as
well as lifting heavy objects. These new tech robots actuators exceed the
strength, speed and efficiency of biological muscle and their flexibility. In
addition to assisting as hydraulic fluid which supports flexible movements, the
use of liquid insulating layer enables robots’ actuators to self-heal from
electrical damage. Another soft actuator that are controlled by high voltage,
also known as dielectric elastomer actuators; it utilizes a solid insulating
layer that fails catastrophically from electrical damage [4-6] (Figure 3).
Figure 3: Illustrates actuators can be designed as soft grippers to handle and manipulate delicate objects, like this raspberry. Image Credit: Keplinger Lab / University of Colorado Boulder [6].
Graphene for Artificial Skin in Self-Healing Robots
Graphene
is a sheet of pure carbon atoms and it is known as world’s strongest material;
it is one million times thinner than paper. It is so thin that it can be viewed
as two dimensional. Although, it’s hefty price, graphene has become most
favorable nanomaterials due to its unique and multipurpose applications. One of
the organs in the human body; skin is known for its fascinating self-healing
properties. Imitating this phenomenon has proved too much of work as manmade
materials lack this technology. Due to stretching or bending and incidental
scratches, artificial skin used in robots are too much susceptible to ruptures
and fissures. In this study a novel solution where a sub-nano sensor uses
graphene to sense a crack as soon as it starts nucleation even after the crack
has spread a certain distance. Scientist subjected a single layer graphene
comprising various issues like pre-existing vacancies and inversely oriented
pre-existing cracks to uniaxial tensile loading till fracture. Once it is
completed, graphene started to heal and the self-healing continued irrespective
of the nature of pre-existing issues in the graphene sheet. Not to mention,
whatever the length of crack, they were all healed; provided the critical crack
opening distance are within 0.3 to 0.5nm for pristine sheet and sheet with
pre-existing defects [7,8].
Wolverine Inspired Material for Self-Healing
Robot
Researchers
at University of California, Riverside designed a novel method of an ionic
conductor, that means material that ions can flow through and it is
mechanically stretchable, transparent and self-healing. These materials have
wide variety of applications in extensive range of fields. It can give robots
to self-heal after mechanical failure. It also extends the lifetime of lithium
ion batteries used in electronics and electric cars; and improve biosensors
that are used in medical and environmental fields. This material was inspired
by wound healing in nature, self-healing materials repair the damage caused by
wear and extend the lifetime and in turn lowering the cost of the device. Ionic
conductors are a class of materials with vital roles in energy storage,
sensors, solar energy conversion and electronic devices.
The
vital problem is the identification of bonds that are stable and reversible
under electrochemical conditions. Traditionally, selfregenerative polymers
utilize non-covalent bonds which makes it difficult because these bonds are
affected by electrochemical reactions that decreases the performance of the
materials. Wang solved that critical problem by utilizing a novel mechanism
that is known as ion-dipole interactions; the forces between charged ions and
polar molecules that are highly stable under electrochemical conditions. In
this method, he joined a stretchable polymer with mobile and high ionic
strength salt to create material with the properties that scientist was
searching. It is a low cost and can be easily produce soft rubber like material
that can stretch 50 times its original length. If it has been cut, it can
completely heal in 24 hours at room temperature. As a matter of fact, after
only five minutes of healing the material can be stretched two times its
original length [9,10] (Figure 4).
Figure 4: Illustrates showing self-healing via ion-dipole interaction. Image Credit: University of Colorado, Boulder [10].
Robots That Can Morph Metal Shapes
Researchers
created a novel hybrid material that is stiff metal, soft and porous rubber
foam that integrates the best properties of stiffness and as well as elasticity
when a change of shape is necessary. This material also has the capability of
self-heal if damaged. This material integrates with the soft alloy called
Field’s metal with a porous silicone foam and the rigidity and load bearing
capability of humans with the capability to drastically alter shape, like an
octopus. In addition to this, its melting point is 144 degrees Fahrenheit, the
major reason Field’s metal was taken because it has no lead in it. The
elastomer foam is immersed into a molten metal then it is placed in a vacuum so
that the air in the foam’s pores are removed and interchanged by the alloy. The
foam had pore sizes of around 2 millimeters that can be adjusted to make a
stiffer or more flexible material. In testing of its strength and elasticity
the material ability was deformed when heated above 144 degrees, then it
regained rigidity when cooled; then it returned to its original shape and
strength when reheated [11,12] (Figure 5).
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Friday, 1 October 2021
Lupine Publishers | Simulation of the Instability of Gas Layer Flow Inside Fluid
Lupine Publishers | Advances in Robotics & Mechanical Engineering
Abstract
The
stability of a thin gas layer flow between two fluid layers moving in the same
or opposite direction is modeled and simulated numerically. A linear stability
is considered for the system using the non-stationary equation array, which
consists of the two onedimensional non-stationary equations of a seventh and
fourth order. The results of the numerical study showed that the thin gas layer
between two liquid layers is unstable to a number of different perturbations of
the flow parameters.
Keywords: Flow, Gas Layer, Liquid, Interface, Linear Stability,
Three Layers, Instability, Interface
Introduction to the Problem
Gas
or vapor layer flow may occur in a number of different physical facilities and
devices [1-3], e.g. in a pool with volatile coolant [4,5]. Also, as a stage of
drop disintegration through the phase of a film flow [6], etc. In fact, the
first two phenomena may occur together in real cases [4,5]. Such liquid - gas
(vapor) interfaces are prone to different types of instability. The jet’s stability
increases in infinite medium by increasing viscosities of jet and medium [7-9].
Instability of thin gas layer between two fluid layers was not reported in the
literature yet.
Problem Formulation
The
aim of paper is studying the phenomenon through the mathematical modeling and
computer simulation. Linear equations for the spatial-temporal dynamics of the
gas-liquid interfaces are derived and the boundary conditions are stated. The
equation array is solved numerically and analytically (for same limit cases),
and several sets of the base states are found, and their linear stability
properties are examined.
Mathematical Model of The System
2-D three-layer flow is considered for
the following physical situation. In equilibrium state supposed to be three layers
moving with constant velocities in the same or different directions. The lowest
layer is considered being in the rest or the coordinate system is touched with
it moving with the same velocity. So that gas layer is moving with respect to
lower layer with velocity U1.
And the upper liquid layer moves with velocity U2 against gas layer or in the
same direction (U2 < 0). It is
assumed that inertia forces are big enough to neglect gravitational forces. And
y=0, y=a are the unperturbed interfaces at the beginning. Gas flow supposed
incompressible. The scheme of a three-layer flow: y=0, y=a – free surfaces of a
gas layer; y=-b1, y=b2 – free surface of
the lower and top liquid layers, U1, U2 – flow velocities. The governing
equations are the continuity and the momentum Navier-Stokes equations, which
can be represented in the following linearized form:
Where V = {U, V}is the fluid velocity field, p is the pressure, t is time, ∇ ≡ (∂x,∂y) , ρ - density, μ - dynamic viscosity and indexes, j = 1, 2, 3 are used for gas (vapor), top liquid and bottom liquid, respectively. Boundary conditions are following: tangential stresses supposed to be negligible at the gas – liquid interfaces, therefore
where hj(x,t) are small-amplitude perturbations of the interfaces of the gas flow layer. The balances of the normal stresses at the interfaces and the augmented kinematics condition are:
where σ2 ,σ3 , are the surface tension coefficients for the low and top liquid layers with a gas layer, respectively. In (4), (5) the capillary forces are taken with the opposite signs because convex and concave for the top and lower surfaces result in capillary pressure in a gas layer different by sign. Slip is neglected at the interfaces:
In unperturbed state the interfaces are the straightforward lines, there is a gas slip at the interfaces. But no-slip is considered by gas flow with the perturbed interfaces having uneven boundaries. The liquid layers supposed to be thick enough to suppress the perturbation inside them:
where b1>>h1, b2>>h2. The boundary conditions are linear in assumption that the long-wave small-amplitude perturbations of interfaces are considered. Boundary layer approximation may be applied for the thin gas layer. Then for gas flow p1=p1(x, t), and the momentum equation in y is omitted. Considering the instability of the interfaces one can integrate the equations (1) with boundary conditions (2)-(9) with respect to y and reduce the boundary problem (1)-(9) to the evolutionary equations for Then it is better to use a dimensionless form. The scale values are chosen as: a, U1, a/U1, p1U21 1 - for the length, velocity, time and pressure, respectively. It is considered that in the unperturbed state the layers move with constant velocities along x. Then dimensionless boundary problem (1)-(9) for perturbations is got in the following form:
where the momentum equation for the gas flow is omitted because a boundary layer approach is adopted for it due to considered thin gas layer. Here Re =U1 a /ν1 - the Reynolds number for gas flow, ν - kinematic viscosity coefficient, ρ12 = ρ1/ ρ2 ,ρ13 = ρ1/ ρ3, ν21=ν 2 /ν1 ,ν 31 =ν 3 /ν1 , U21 =U2 /U1 . Here U21 characterizes the liquid to gas velocity ratio. Dimensionless boundary conditions (2)-(9) are
Mathematical Model of the System
From
(10)–(17), derivation of the evolutionary equations for oscillations of the
boundaries of gas layer was done [9], with polynomial approximation of the
transversal velocities in the layers. The following differential equations for
the perturbations of boundaries of layers were obtained [9] as:
Problem Solution
Analysis
of the system (18) - (21) allows stability study of the boundaries of gas flow.
The partial differential equation array includes the derivatives from
perturbations of the gas free surfaces by time t and coordinate x. It is seen
that derivatives are of the higher orders up to the eighth order; therefore it
is difficult for solving. Four equations totally, two functions sought, which
is a consequence of the approximations applied for the profiles of transversal
velocities and pressures of the liquid layers. As far as two last equations are
autonomous, they can be solved independently, considering for example the
simple harmonic waves in the form
where j=1,2, i = −1 , x j – constants, the initial amplitudes of the perturbations, kj, wj- the wave numbers and frequencies of the oscillations, φj – the initial phases of perturbations. Afterward, substituting the obtained solution into the other two equations of the system, we can get dispersion equations for computing the frequencies of perturbations wj = wj (kj) depending on the wave numbers. The perturbations of the top and lower boundaries are interconnected and can differ only by the initial phases φj, k1= k2= k, w1 = w1 = w:
With account of the above, substituting (22) into (20), (21) after the contraction of the exponent and the amplitude xj (the equations are linear homogeneous in terms of the perturbations), we obtain:
In the momentum equation for the second phase (upper liquid layer) the terms ln β2 are kept, becauseβ2 >> 1 can be by: ln β2~ β2 (e.g., β2 =100 , ln β2 ≈ 4,6 ; 2 β =10 , lnβ2 ≈ 2,3 ; β2 =1000 , lnβ2 ≈ 6,9 ; 4 β2 =10 , ln β2 = 9, 2 obviously the terms with 2 lnβ ~ 1 , when β2 ~ 10 , but ln β2 ~ 10 for β2 in a substantially wide range of β2 . Thus, the terms with ln β2 can be omitted when β2 ~ 10 and β2 ~ 1000 and higher, and around β2 ~ 100 they can be substantial and depending of specific values because they are multiplayers with bigger ones than β2 ). Further work must be done with computational experiment and analysis of the results obtained. The model thus derived may be useful in the investigations of some physical problems including stability of the vapor layer around the hot particle during its cooling in a volatile liquid, for revealing the peculiarities of the heat transfer critical heat flux. Computer Simulation of the Free Boundaries of Gas Layer Parameters of the available surface waves on the interface of gas layer with the liquid layers are computed from solution of the equation array (23), (24): k1= k2= k, w1 = w2 = w. Both, wave numbers and frequences of the oscillations are complex in a general case. For searching these values, the Flexed platform was used to prepare the computer program and provide the numerical simulation. The computer program was developed in the following form:
TITLE
‘3 fluids’ { the problem identification }
Select
ngrid = 5 errlim = 0.001
variables
wr1
wi1 wr2 wi2
COORDINATES
cartesian1 { coordinate system, 1D,2D,3D, etc }
definitions
{ system variables }
b1
= 1 b2 = 100 Re3 = 100 Re2= 12000 nu21 = 0.5
EQUATIONS
{ PDE’s, one for each variable }
{ one possibility }
BOUNDARIES
{ The domain definition }
REGION
‘domian’ { For each material region }
start
(0) line to (10)
MONITORS
{ show progress }
PLOTS
{ save result displays }
elevation(wr1,wi1,
wr2, wi2) from (0) to (1)
elevation(wr1,wi1,
wr2, wi2) from (0.5) to (1.5)
elevation(wr1,wi1,
wr2, wi2) from (1) to (2)
elevation(wr1,wi1,
wr2, wi2) from (2) to (3)
elevation(wr1,wi1,wr2,wi2)
from (0) to (10)
END
Here the values wr1, wi1, wr2, wi2 mean
the real and imagine parts of the frequencies of perturbations. The argument x
in the program means wave number k. The other parameters are: β1 = 10, β2 = 0.1 (thin gas
layer), Re3 = 106, Re2 = 5·104 (Re2= Re· 21 v ),
21 v = 17.2 ·10-6. The results of
numerical simulation with the above computer program are presented below in
Figure 1 as the graphs for real (wr1, wr2) and imagine (wi1, wi2) parts of the
w1, w2 versus the wave
number k (x in figures):
Figure 1: The values of frequences w1, w2 (wr1, wi1, wr2, wi2) against wave number k b1 = 10, b2 = 0.1.
As far as equations (23), (24) are
satisfied simulataneously, w1=w2 is available for the above stated
parameters approximately by k = 0.5, which corresponds to the long-wave
perturbations of the interface. The short waves do not satisfy the equation
array and physically it is understandable because the short waves are fast
decreasing with time. For the representing the corresponding surface waves ,
the following computer program was used:
TITLE
‘3 liquids’ { the problem identification }
Select
ngrid = 5 errlim = 0.01
Variables
e
COORDINATES
cartesian1 { coordinate system, 1D,2D,3D, etc }
definitions
{ system variables }
wr1 = 2*10-5 wi1 = 3*10-5 k = 0.5
EQUATIONS
{ PDE’s, one for each variable }
e
= exp(wi1*t)* (cos(k*x - wr1*t)
BOUNDARIES
{ The domain definition }
REGION
‘domian’ { For each material region }
start
(0) line to (10)
TIME
0 TO 100 by 0.4 { if time dependent }
MONITORS
{ show progress }
PLOTS
{ save result displays }
for
t = starttime by ( endtime - starttime) / 200 to endtime { snapshots }
elevation(
e) from ( 0) to ( 20) as “e”
history
(e) at (0)
END
The results of computation are presented
in Figure 2, where from is seen that the wave is nearly of the same amplitude
(just oscillation) by these parameters, only the thinner is gas layer, the
higher are oscillations being still stable by these parameters. For the second
case (β1 = 1,β2 = 0.1) the
parameters are: wr1 = 2*10-5,
wi1 = 3*10-5, k = 1.51, so that the
perturbation of the interface is very slowly growing by time being nearly
stationary (phase velocity of the surface wave is approximately 1.3*10-5). The other results
support the mentioned. Calculation for t = 7.5*104 gave the same
result as for t = 5*104.
Both correspond to complete disintegration of the gas layer. Both graphs (by
time at x=0 and by x depending on time show the same results of the system’s instability).
Figure 2: Wave ei(k1x−ω1t+φ1).
Figure 2 Wave ei(k1x−ω1t+φ1) against time by x
= 0 and against x at the moment t = 5*104 (β1 = 1, β2 = 0.1).
Instability is developed up to destroying the system on the drops and fragments
in the time about t=2 (about ten times growing of the oscillations by
amplitude; the time is dimensionless; therefore it depends on parameters: width
of the layer and velocity of the flow). Red colored are parameters ω in the
table below, which correspond to the growing (unstable) perturbations, while
the blue ones - to the stable oscillations.
Using
the results obtained one can study the influence of the parameters on stability
of the gas layer moving between the liquid layers. As shown above, mostly it is
unstable. The results may be treated as instability of the vapor layer
surrounding the hot liquid drop, which is cooled down in a volatile coolant,
for example under severe accident at the nuclear power plant (Table 1).
Conclusion
As
numerical simulation revealed, all values of the ω are complex. The imagine
part of frequency ω means that by positive values of ω the perturbations are
growing by time (instability) or fading (stability). By real frequency when
imagine part is absent, the perturbations are just oscillating interfaces
between the layers. Thus, we have got many parameters of the perturbations,
which lead to the breaking the gas layer.
For example, by β1=2, β2=2 and v=10, the system
is stable. Mainly stable regimes are observed by the next parameters:
Table 1: Calculated values of the wave numbers k and frequencies ω.
β1=2, β2=0.5, v=100;
β1=0.5, β2=2, v=10;
β1=1, β2=0.5, v=10;
β1=2, β2=2, v=100;
β1=2, β2=2, v=1000;
β1=0.5, β2=0.5, v=10.
But in reality the system is unstable if there are just a few available unstable oscillations of the interface because many of them are present. Therefore, the conclusion is that gas layer moving between the liquid layers is unstable and the most unstable waves are of the length a few width of the gas layers.
https://lupinepublishers.com/robotics-mechanical-engineering-journal/pdf/ARME.MS.ID.000123.pdf
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