Year-2015http://dspace.iitrpr.ac.in:8080/xmlui/handle/123456789/2982024-03-28T08:37:49Z2024-03-28T08:37:49ZAnalyses of lattice hydrodynamic models in traffic flowRedhu, P.http://dspace.iitrpr.ac.in:8080/xmlui/handle/123456789/26142021-09-06T07:17:40Z2021-09-06T00:00:00ZAnalyses of lattice hydrodynamic models in traffic flow
Redhu, P.
The present thesis is solely concerned with the development and analyses of mathematical
models to understand traffic flow dynamics. We adopt the lattice hydrodynamic approach
to model traffic phenomena, in which space is discretized in the form of lattices. In this
work, we investigate the phenomenon of traffic congestion under the consideration of
different important aspects such as driver’s behavior, passing phenomenon, interruption,
gradient highways and multi-phase transition on one-dimensional single lane highway
etc. Furthermore, single lane traffic flow model is also extended for two-lane system
by incorporating the lane-changing behavior and the effect of driver’s behavior has been
analyzed. The thesis also incorporates traffic models for networks on square as well as
triangular lattices. All the proposed models are examined theoretically through linear as
well as nonlinear stability analysis using the reductive perturbation method. The Burger,
KdV and mKdV equation are derived near the critical point from nonlinear stability analysis
and the formation of traffic congestion in terms of kink-antikink soliton density waves is
explained. The critical boundaries are calculated theoretically for which kink solution of
mKdV equation exists. To verify the theoretical results, numerical simulation is carried
out by using finite difference scheme. The effects of sensitivity as well as other important
parameters are discussed thoroughly and the results are also compared with those reported
in the literature for specific choices of parameters. It is expected that LH models proposed in
this thesis provide a certain degree of improvement to the existing models. We conclude the
overall contribution of proposed work in traffic flow theory and provide some ideas about
future extensions.
2021-09-06T00:00:00ZBoundary value problems arising in multi-layered fluid systemPanda, S.http://dspace.iitrpr.ac.in:8080/xmlui/handle/123456789/7822018-03-20T10:46:30Z2016-07-22T00:00:00ZBoundary value problems arising in multi-layered fluid system
Panda, S.
Boundary value problems (BVPs) occur in a natural way while studying the scattering
of water waves as well as the fluid flow problems. The objective of the thesis is to solve
such BVPs by using the most appropriate mathematical techniques and to analyze: (i)
scattering of small amplitude water waves by different types of undulations present at
the porous bottom in a two-layer fluid of finite depth, where the upper layer is either
free to the atmosphere or covered by a thin ice-sheet or affected by the surface tension;
(ii) the behavior of the free-surface as well as the interfaces at the outset in the case
of the flow of fluid in a multi-layered channel having an arbitrary bottom topography.
It is assumed that the fluid is inviscid, incompressible and immiscible with constant but
different densities; and the motion of the fluid is irrotational and simple harmonic in time.
In Part-I of the thesis, various problems involving scattering of water waves in a two-
layer fluid are considered for their solutions where the upper layer is either free to the
atmosphere or covered by a thin ice-sheet or affected by the surface tension. Depending
upon the angle of incidence, the problem is one of these kinds: one describing the scatter-
ing of waves when the progressive waves incident normally to the undulating bottom, and
the other describing the scattering of waves when the progressive waves incident obliquely.
In each situation, the physical problem formulated as mixed and coupled boundary value
problem to determine the velocity potentials corresponding to each layer of the fluid. The
governing partial differential equation happens to be Laplace’s equation for the case of
normal incidence, whereas it is Helmholtz equation for the case of oblique incidence with
mixed boundary conditions at the top surface and at the porous bottom and two interface
conditions out of which one is mixed boundary condition. Due to the mixed boundary
condition at the interface, the BVPs become coupled. As the fluid region extends to infin-
ity, a far-filed condition in each layer arises which affirms the uniqueness of the problem.
The coupled and mixed BVP is reduced to a simpler coupled BVP of the first-order by
employing a perturbation analysis. The simpler coupled BVP is uncoupled which gives
rise to two independent BVPs. These independent BVPs are solved by using the Fourier
transform technique and residue theorem to derive the first-order velocity potentials.
These potentials are utilized to determine the first-order reflection and the transmission
coefficients. These coefficients are obtained in terms of the integrals involving the shape
of the undulating porous bottom. Different types of shape functions are considered to
evaluate these integrals explicitly. The numerical values of the first-order reflection and
transmission coefficients for various system parameters are derived and shown graphically
for a special kind of bottom topography, namely a patch of sinusoidal ripples due to its
applications in the coastal and marine engineering. The graphical forms illustrate the
transformation of the incident wave energy from one layer to another layer. In addition,
the energy identity, an important feature of the study involving scattering of water waves in a two-layer fluid, is investigated in detail with the help of the Green’s integral theorem.
This identity provides the correctness of the analytical and numerical results derived in
this thesis. The Fourier transform method is found to be a comparatively easier method
for solving the scattering problems. It may be emphasized that, when the density of the
upper layer fluid is equal to the density of the lower layer fluid, the two-layer fluid problem
reduces to a single-layer fluid problem which is also investigated here. The results devel-
oped here are expected to be helpful for a large class of scattering problems in a two-layer
ocean with an uneven porous bottom in the areas of coastal and marine engineering.
In Part-II of the thesis, various problems involving the flow of fluid in a channel are
considered for their solutions. Here the behavior of the free-surface as well as the interface
profiles (for multi-layer fluid) which are unknown at the outset, are analyzed. First, the
problem involving the flow of an inviscid and incompressible fluid in a single-layer channel
having small obstruction is studied, and then the problem involving two-layer flow is
studied to determine the analytical expressions for the profiles of interface and the free-
surface. Further, the two-layer flow problem is generalized as the three-layer flow problem
as the single or the two-layer approximation becomes insufficient due to the continuous
stratification of the fluid. The BVPs arising in a natural way are solved using perturbation
analysis in conjunction with Fourier transform technique. In the case of the flow in a three-
layer fluid, the following flow problems are studied: (A) when the uppermost fluid layer is
bounded by a rigid lid and (B) when it is free to the atmosphere. In this case, in order to
study the influence of natural and individual variation of the bottom profile on the essence
of the interface profiles, two different kinds of bottom profiles, such as concave and convex
are considered in both the problems separately. In both problems (A) and (B), the nature
of the roots of the dispersion relation, which is an important relation of the study involving
fluid flow, is investigated in detail using the Rouche’s theorem. The numerical results are
tabulated and demonstrated in graphical forms to understand the effect of some important
physical quantities on the behavior of the interfaces. It is observed that the interfacial
profiles are oscillatory in nature, representing waves of variable amplitude with different
wave numbers which lead to several interesting features like wavy solutions, beating-like
behavior, downstream resonances etc. These phenomena are noticed in this study, which
are not reported in earlier studies. In addition, it is observed here that the interface profiles
exhibit a wave-free region at the upstream of the obstacle followed by a wavy region at
the downstream of the obstacle. These studies are based on the linear theory. An effort
has also been made in this thesis to solve a nonlinear flow problem involving free-surface
flow over arbitrary bottom in a single-layer fluid. A simple numerical approach for solving
Fredholm integral equations of the second kind is developed here. This new method helps
in finding the solution of this nonlinear flow problem. This nonlinear flow problem is
formulated mathematically in terms of a nonlinear BVP which is reduced to a Dirichlet problem after using certain transformations. After utilizing a suitable application of
Plemelj-Sokhotski formulae, the Dirichlet problem is solved when a pair of second kind
Fredholm integral equations are solved. The new approximate method developed here
is utilized to solve the coupled integral equations and hence the free-surface profile is
determined. A number of observations are made to illustrate the effect of nonlinearity.
The effects of the Froude number and the arbitrary bottom topography on the free-surface
profile are discussed here. In addition, the nonlinear results are compared with the results
obtained by using the linear theory.
The study in the thesis may be helpful for handling different situations arising in the
broad area of ocean engineering, atmospheric sciences and related branches of mathematical physics.
2016-07-22T00:00:00ZErosion-corrosion corrosion studies of nanostructured Ni-Cr Ni Cr coatings on SAE 213-(T22) 213 and SA 516 (Gr -70) steelsKumar, M.http://dspace.iitrpr.ac.in:8080/xmlui/handle/123456789/7802018-03-20T10:46:16Z2016-12-21T00:00:00ZErosion-corrosion corrosion studies of nanostructured Ni-Cr Ni Cr coatings on SAE 213-(T22) 213 and SA 516 (Gr -70) steels
Kumar, M.
Fireside degradation of boiler tubes in coal-fired water tube boilers is a combined
effect of erosion as well as corrosion. The corrosion products (oxides and sulfides) are
formed on boiler tubes due to chemical reactions with the combustion gases,
simultaneously the flue gases present in the boiler environment erode these corrosionproducts
deposited on the tubes. Fireside erosion-corrosion of boiler tubes leads to
continuous thinning of the boiler tubes in the working environment, which can further
result into instantaneous rupture of the tubes. Erosion-corrosion is recognized as the main
cause of downtime (50-75% of their total arrest time) at power-generating plants, which
leads to enormous economic losses (Koch et al., 2002; Hidalgo et al., 1997). Keeping in
view of these crucial facts, erosion-corrosion control of boiler tubes has invited
considerable attention and among the various alternatives the thermal sprayed coatings
have the potential to provide suitable protection to boiler steels from the aggressive
fireside corrosion (McCune et al., 1995). Among various thermal spray coating
techniques, high-velocity oxy-fuel (HVOF) spraying is a frequently considered process to
provide high temperature E-C protection to boiler tube. Further, a new entrant in the
category of thermal spray processes, namely cold-spray process has great potential to be
used for such applications. Cold-spray process works well below the melting point of
feedstock powders (Papyrin et al., 1996). The major role played in deposition of coating
is by the momentum transfer from the supersonic gas jet to powder particles, results in
high particle jet. These powder particles on striking with substrate surface plastically
deformed, to form interlinked splats resulting in a surface coating. No oxidation of
coating powders takes place during in-flight and hence no phase transformation occurs
during deposition process. These features give cold-spraying process a capacity to
develop nano-structured coatings.
In the current investigation, hot corrosion behaviour of uncoated and coated
boiler tube materials namely SA213-T22 and SA 516-Grade 70 was studied. The nanoparticles
of Ni and Cr were synthesized using bottom-up and top-down approaches. These
nano-particles were further characterized using several characterization techniques such
as XRD, SEM/EDS, TEM, DLS and CHNS-O analyses. The average particle size of
oxide-free Ni nano-particles synthesized by chemical route was found to be 29 nm, with a
spherical morphology. Average particle size of Ni and Cr nano-particles synthesized by
mechanical milling (top-down approach) was found to be 67 nm and 59 nm respectively, with irregular flake-type morphology. Four novel variants of nanocrystalline Ni-20Cr
powders were synthesized by blending nano-sized and micron-sized powders in a
planetary ball mill, in such a way that overall wt.% Ni:Cr was maintained as 80:20.
Average particle size of four different variants of Ni-20Cr nanocrystalline powders
synthesized by mechanical route (designated as Powders A, B, C and D), was found to be
14 µm, 6 µm, 13 µm and 11 µm respectively. XRD and TEM analyses have been carried
out to confirm the nanocrystallinity of the synthesized powders and the crystallite size
was found to be 8 nm, 12 nm, 13 nm and 10 nm respectively. Then, these nanocrystalline
powders were deposited on the selected substrate steels using HVOF and cold-spray
techniques. The developed HVOF-sprayed coatings have been designated as AHT, BHT,
CHT, DHT, AHS, BHS, CHS, DHS, whereas cold-sprayed as ACT, CCT, DCT, ACS,
CCS, DCS; here A, B, C, D refer to the coating variants, H to HVOF-spray, C to coldspray,
T to T22 steel substrate and S to SA 516 steel substrate. It has been found that the
deposited coatings could maintain the nanocrystalline structure similar to that of
feedstock powders, although slight grain growth occurred during deposition process. The
developed coatings were subsequently characterized with regard to their metallurgical
and mechanical properties.
The HVOF-sprayed coatings in general, were found to have the presence of Ni
and NiO phases. The presence of NiO phase may be due to in flight oxidation of Ni
particles during deposition process. On the other hand γ-Ni was observed as the main
phase in all the cold-spray coatings without the formation of NiO or any other oxide. In
this way, cold-spray coatings were found to be oxide-free, which is useful attribute from
the point of view of high temperature corrosion resistance. Surface and cross-sectional
optical and SEM micrographs of the investigated HVOF-spray nanostructured coatings
indicated a typical splat-like morphology, which led to the formation of a lamellar crosssectional
microstructure. Most of the splats/particles exhibited a flattened appearance,
which is an indication of severe plastic deformation during deposition process. The
coatings in general were found to have a continuous contact with the steel substrate. The
investigated cold-sprayed coatings had a dense morphology, in general, formed as a
consequence of proper coalescence of feed stock powder particles. It was further
observed from the X-ray mappings that the inter-diffusion of various elements between
the substrate and the HVOF/cold sprayed coatings was found to be marginal. The XRD
results were well supported by the surface as well as cross-sectional SEM/EDS analysis. TEM analysis revealed the consistent distribution of grain size indicating that the nanocharacteristics
of both the Ni-rich phases and Cr-rich phases were well preserved in the
cold-spray coating. Various mechanical properties such as microhardness, scratch
resistance, elastic modulus, and fracture toughness of as-sprayed coatings were studied.
The average microhardness of HVOF and cold-sprayed coatings on T22 and SA 516 steel
was found to be higher than the conventional Ni-20Cr coatings (micron-sized) on the
same steels. Elastic modulus of the coating is the indicator of the stiffness of the coatings.
HVOF-sprayed coatings on T22 steels had shown stiffer behavior in comparison to coldsprayed
coatings on T22 steels. But in case of SA 516 steels, cold-spray coatings had
offered more stiffness in comparison to HVOF-spray coatings. The fracture toughness of
the HVOF-spray coatings was found to be quite high in comparison to cold-spray
coatings.
The cyclic air oxidation studies of uncoated and coated steels were conducted at
900ºC for 50 cycles. The analyses regarding the oxide scale thickness, XRD, SEM/EDS
and X-ray mapping analyses of the oxidized samples have been carried out. T22 steel
showed a relatively higher air oxidation resistance in comparison with SA 516 steel,
which may be attributed to the presence of Cr (2wt.%) in the former steel. Amongst all
the developed coatings (HVOF and cold-sprayed) on T22 steel, the cold-sprayed coatings
in general, showed comparatively high oxidation resistance. The ACT coating was found
to have shown highest resistance to oxidation, which may be attributed to its finest grain
(18 nm) size among all the coatings on T22 steel. Furthermore, this coating was even
found to have a better oxidation resistance (two-fold) in comparison with the reported
cold-sprayed Ni-20Cr microstructured coating on the same steel (Bala, 2010). Further it
has been found from the cross-sectional EDS and x-ray mapping analyses of all the coldsprayed
T22 steels that no internal oxidation of substrate has taken place and the basic
elements have been preserved, with an exception of DCT coating. Overall it was
observed that with the increase in grain size of the coatings, the capability to offer
oxidation resistance decreased both for the HVOF and cold-spray coatings. The surface
XRD analysis confirmed the presence of mainly NiO and Cr2O3 phases in the scale of all
the investigated coatings, with the exception of DHT coating. These oxides (NiO and
Cr2O3) may partially inhibit oxidation of substrate steels by blocking the diffusion of
reacting species towards the substrate steel as has been suggested by Nicoll and Wahl
(1983). However in case of DCT coating, O was penetrated to substrate region. In case of BHT, CHT and DHT coatings small superficial cracks were found near edges during
oxidation studies. The cracking and some minor spallation may be due to thermal shocks
due to difference in heat expansion coefficients of oxides, coatings and the substrate
(Rapp et al., 1981 and Liu et al., 2001). But overall no depletion of basic elements was
observed from the substrate steel.
The cold-sprayed coatings outperformed the HVOF-spray coatings and showed
high erosion-corrosion (E-C) resistance to base steels, amongst the investigated HVOF
and cold-spray coatings on T22 steel. This may be attributed to the relatively lower oxide
content and low porosity present in the cold-spray coatings. Moreover, the relatively
higher hardness of the cold-sprayed coatings might have also imparted higher erosion
resistance to coatings in comparison with HVOF-sprayed coatings. In terms of thickness
loss, CCT and DCT coatings offered the highest E-C resistance. Further, the performance
these coatings were found to be better than conventional Ni-20Cr coatings (Bala, 2010).
Similarly AHT, ACT and DHT coatings were also successful to reduce the E-C of T22
steel. However for the other two variants, the scale-substrate interface was found to be
severely damaged and some cracks were seen in the coating area. Therefore, these
coatings could not provide necessary protection to the steel.
Amongst all the developed HVOF and cold-sprayed coatings on SA 516 steel, the
cold-sprayed coatings in general have shown high temperature oxidation resistance in
comparison to HVOF-sprayed coatings, except AHS coating, which offered highest
oxidation resistance among the investigated coatings on SA 516. AHS coating showed
only a marginal weight change (2.96 mg/cm2
) till the end of the experimentation and was
able to reduce the weight gain of bare steel by 98.4%. This may be due to the strong
presence of NiO and Cr2O3 phases. CCS coating was found to be the second best
performing coating, which has the additional presence of a spinel phase NiCr2O4 in its
oxide scale, alongwith NiO and Cr2O3. It has been reported that the spinel phase
(NiCr2O4) has smaller diffusion coefficients of the cations and anions than those in their
parent oxides (Chatterjee et al., 2001). Furthermore, it was observed that the CCS coating
outperformed its counterpart cold-sprayed microstructured Ni-20Cr coating under similar
conditions of oxidation testing (Bala, 2010). Both DCS and ACS coatings were also
found to be better performing in comparison to the micron-sized Ni-20Cr coating. This
reduction in oxidation rate in comparison to microstructured coatings may be attributed to
rapid promotion of selective oxidation of Cr to form denser Cr2O3 scale due to enhanced grain boundary area (Chen et al., 1999; Peng et al., 2005). This was followed by DHS,
CHS and BHS coatings in terms of oxidation resistance. In case of BHS and CHS coating
the scale-substrate interface was damaged, so were not able to stop internal oxidation.
Amongst all the investigated HVOF and cold-sprayed coatings on SA 516 steel,
the cold-sprayed coatings were found to be relatively more effective to reduce the E-C
rate, similar to T22 steel cases. In terms of thickness loss the CCS and DCS coatings
provided the highest E-C resistance, followed by AHS, CHS, DHS and ACS coatings.
The E-C resistance trend of HVOF-spray coatings could be co-related with grain size of
the coating, with the exception of BHS coating. For all other cases, it was observed that
E-C resistance increased with decrease in grain size of the coating. However, BHS
coating showed the highest corrosion rate (83 mpy) irrespective of its lower grain size,
which may be attributed to its lowest thickness. It is worth to mention that only 50 µm
coating thickness could be achieved in this case. Due to low average particle size of
feedstock powder B (6 µm), the flowability of the powder became the major issue and
hence the lowest thickness of the coating was achieved in BHS case.
Based upon the overall results of the current study, it has been recommended that
CCS coating may be the best choice for the given boiler application. It is pertinent to
mention that the cold-sprayed coatings in the current work were developed by a costeffective
approach in which air was used as working medium (powder carrier gas),
whereas during development of conventional cold-sprayed coatings (micron-sized) a high
purity and costly helium gas was used (Bala, 2010). In this way the current research
offers cost-effective solution to prospective boiler industry.
2016-12-21T00:00:00ZNon-invasive detection and differentiation of skin cancer stages–a numerical studyBhowmik, A.http://dspace.iitrpr.ac.in:8080/xmlui/handle/123456789/7792018-03-20T10:46:19Z2016-12-21T00:00:00ZNon-invasive detection and differentiation of skin cancer stages–a numerical study
Bhowmik, A.
2016-12-21T00:00:00Z