OPTIMIZATION OF RADIAL FAN IMPELLER USING FINITE ELEMENT ANALYSIS A PROJECT REPORT Submitted by KISHORE KANNA.B 40401114020 MOHAMMED MOHAIDEEN.M 40401114033 PANDIARAJ.T 40401114039 SATHISH KUMAR.K 40401114049 in partial fulfillment for the award of the degree of BACHELOR OF ENGINEERING in MECHANICAL ENGINEERING B.S.ABDUR RAHMAN CRESCENT ENGINEERING COLLEGE, CHENNAI-48
121
Embed
Optimization of Radial Fan Impeller Using Finite Element Analysis-report[1]
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
OPTIMIZATION OF RADIAL FAN IMPELLER
USING FINITE ELEMENT ANALYSIS
A PROJECT REPORT
Submitted by
KISHORE KANNA.B 40401114020 MOHAMMED MOHAIDEEN.M 40401114033PANDIARAJ.T 40401114039SATHISH KUMAR.K 40401114049
in partial fulfillment for the award of the degree
of
BACHELOR OF ENGINEERING
in
MECHANICAL ENGINEERING
B.S.ABDUR RAHMAN CRESCENT ENGINEERING COLLEGE,
CHENNAI-48
ANNA UNIVERSITY: CHENNAI 600 025
MAY 2005
BONAFIDE CERTIFICATE
This is to certify that the project work entitle “OPTIMIZATION OF
RADIAL FAN IMPELLER USING FINITE ELEMENT ANALYSIS”
is a Bonafide record of the work done by
KISHORE KANNA.B - 40401114020
MOHAMMED MOHAIDEEN.M - 40401114033
PANDIARAJ.T - 40401114039
SATHISH KUMAR.K - 40401114049
Students of B.E., (Mechanical Engineering) of B.S ABDUR
RAHMAN CRESCENT ENGINEERING COLLEGE, Chennai at Ranipet.
During the period from 31-01-05 to 28-02-05.
We wish them all the success in their future endeavour.
For BHARAT HEAVY ELECTRICALS LIMITED
Mr. R.BABU M.Tech (IIT-Madras) Mr.S.PARAMANANTHAM
Deputy Manager (Fans) H.R.D.Officer
BHEL-BAP BHEL-BAP
Ranipet Ranipet
ANNA UNIVERSITY: CHENNAI 600 025
BONAFIDE CERTIFICATE
This is to certify that the project report ‘OPTIMIZATION OF RADIAL
FAN IMPELLER USING FINITE ELEMENT ANALYSIS’ is the
FIG.26- OPTIMIZED BACK PLATE (BOTTOM) STRESS PLOT 60
FIG.27- OPTIMIZED BACK PLATE (TOP) DEFLECTION PLOT 61
FIG.28- OPTIMIZED BACK PLATE (TOP) STRESS PLOT 61
FIG.29- OPTIMIZED BLADE DEFLECTION PLOT 62
FIG.30- OPTIMIZED BLADE STRESS PLOT 62
FIG.31- OPTIMIZED COVER PLATE DEFLECTION PLOT 63
FIG.32- OPTIMIZED COVER PLATE STRESS PLOT 63
FIG.33- OPTIMIZED RING DEFLECTION PLOT 64
FIG.34- OPTIMIZED RING STRESS PLOT 64
FIG.35- OPTIMIZED FLANGE DEFLECTION PLOT 65
FIG.36- OPTIMIZED FLANGE STRESS PLOT 65
LIST OF TABLES
TABLE 2.1- ELEMENT TABLE 19
TABLE .5.2- REAL CONSTANTS FOR THE MODEL 43
TABLE.6.1- OPTIMIZATION TABLE 49
TABLE.7.1- DIMENSIONS FOR THE MODEL 66
NOMENCLATURE
N - rpm
D - Fan diameter (mm)
µ - dynamic viscosity
Ns - Specific speed
Q - Volume flow rate (m3/sec)
gH - specific energy (J/kg)
P - Pressure rise (pa)
ρ - fluid density (kg/m3)
CHAPTER 1
INTRODUCTION
CHAPTER1
INTRODUCTION
1.1 Organization Profile
M/S. BHARAT HEAVY ELECTRICAL LTD., popularly
known as BHEL is today, the largest engineering and manufacturing
enterprise of its kind among the public sector undertakings in India. The
company provides products, systems and services in the field of energy and
transportation for domestic and export markets.
The company ranks amongst the worlds top 10 organizations
engaged in the manufacturing of power plant equipment. About 50
countries, extending from USA in the west to Australia and New Zealand in
the far east are BHEL’s customers.
1.2 BHEL - BOILER AUXILIARIES PLANT - RANIPET
BHEL – Trichy launched its phase III expansion for
augmentation of manufacturing capacity to 4,000 MW for boilers and
auxiliaries at Ranipet Tamilnadu in 1982.
The product profile of BAP, Ranipet is
Fans – Radial, Axial, Impulse and Axial reaction
Electrostatic precipitators
Air preheater (Regenerative type)
These auxiliaries play a vital role in the thermal power plants.
There are 43 ancillaries established adjacent to the plant .BHEL gives by
way of technical , raw material and quality control procedure , BAP Ranipet
has technical collaboration with M/S K.K.K, West Germany for fans .
BAP at Ranipet provides direct employment to about 3,000
employees and indirect employment of over 10,000 employees. BHEL is
certified with ISO 9001 and ISO 9002 by BVQI.
1.8 About the Project.
This project has been done to predict and give the results of a
Radial fan impeller under physical operating conditions.
The Radial fan impeller is analyzed before the performance
testing and installation. Stress analysis is performed to find the maximum
stress values. These analysis are done by ANSYS.
In this project static and optimization of fan impeller thickness
have been performed during the analysis using the software.
In static analysis the maximum stress, strain values for the
required boundary conditions are found. In optimization, the impeller
thickness is reduced or optimized without changing or violating the
maximum stress values. So that the weight reduces and hence the cost of the
product also reduces.
HARDWARE REQUIREMENTS
Processor : PENTIUM III
CPU speed : 400Mhz
HDD : 20GB
Main memory capacity: 159MB
SOFTWARE REQUIREMENTS
ANSYS 5.4
1.9 About the Fan
A fan is a turbo machine used for energy transfer. It can be defined as a rotating machine with a bladed impeller, which maintains a continuous flow of air (or) gases.
Fans usually consist of a single rotor with or without a stator element and cause a rise in pressure of the flowing fluid.
PRINCIPLE OF WORKING:
The principle involved is that the mechanical energy owing to the rotation of the fan is converted into the fluid energy (in the form of pressure rise).
Fans obviously consume power as they rotate with the help of prime mover and energize the flowing fluid.
1.5 CLASSIFICATION OF FANS:
1.5.1 ACCORDING TO PURPOSE:
1. Primary Air Fan :( PA FAN)
Primary air fans supply the air needed to dry and transport pulverized coal to the furnace of direct-fired boiler.
2. Forced Draught Fan: (FD FAN)
The forced draught fans supply the air-required for the combustion of fuel and normally handle stoichiometric plus excess air required for the satisfactory burning of fuel.
3. Induced Draught Fan: (ID FAN)
The induced draught fans draw the products of combustion from the boiler while creating sufficient draught (negative pressure) in the furnace for balanced draught operation.
1.5.2 ACCORDING TO FLOW OF AIR:
1. Radial Fan:
A radial fan is a one in which the flow enters along the axis and leaves in the radial direction along the blades. It can be used for PA, FD and ID applications.
Based on the configuration of the blade with respect to the direction of rotation of the impeller (AS SHOWN IN THE FIG.) it is called backward curved, forward curved and radial bladed impeller
FIG. 1.1
2. Axial Fans:
An axial fan is a one in which the main flow is along the axis of
rotation both at entry and exit.
2 < 90 2 = 90 2 > 90
Based on the profile these fans are mainly classified into two
types namely,
I Axial Profile Impeller: (AP IMPELLER)
In this type, the impeller has a central hub which is spherical in
nature and has blades with individual shafts located along the periphery.
The hub is a high precision part which is ball turned to get a curved
smooth profile. The individual blades of the impeller are driven with
the help of hydraulic mechanism.
II Axial Non – Profile Impeller: (AN IMPELLER)
In this type, the impeller has a central hub, which is of
hemispherical nature and has blades curved at a fixed angle and welded
to the hub as in case of its radial counterpart.
Both the fans described above have an inlet guide vane (IGV)
and an outlet guide vane (OGV) along with a diffuser at the exit.
AEROFOIL BLADED RADIAL FAN - A GLANCE
An aerofoil bladed radial fan consists of blades, which are
profiled, in an aerofoil shape as shown in the figure below:
FIG .1.2
1.6 Advantages of an Aerofoil Bladed Fan:
a. Since the aerofoil is a profile curved body, it ensures a
smoother flow than a blunt body and hence no flow separation
thereby minimized losses
b. Because of higher efficiency than normal plate bladed impeller
it consumes less power and hence it is economical.
c. An aerofoil bladed fan has the higher half – load efficiency like
an axial fan and the rigidity of that of a radial fan and hence the
combined feature of both.
But the aerofoil bladed is mostly employed as primary air fan.
1.7 CONSTRUCTIONAL FEATURES OF A RADIAL FAN:
The fan as a whole can be divided in to some major sub –
assemblies.
1. SPIRAL CASING:
The spiral casing consists of two parallel sidewalls, spiral wall,
Suction Chamber and inlet cone. It is split horizontally along the shaft
axis plane; if necessary the upper portion will also be vertically split off
at the center so that impeller installation is easy. The inlet cone and the
suction chamber are welded to the sidewalls.
2. IMPELLER:
The impeller is a completely welded structure. It consists of a
center plate (or) back plate, cover plate and blades. The blades are
welded between the back plate and the cover plate. Proper welding
sequence is followed to have minimum distortion.
3. SHAFT:
The shaft is a hollow tube with 2 endpins shrunk-fit at the 2
ends is welded. Torque is transmitted through the fit and the weld is only
for securing purpose. The tube is controlled at the inside diameter. The
shaft ends are machined after welding. A flat split ring is welded on to
the shaft tube for taking up the shaft flange. The complete shaft is
dynamically balanced.
4. BEARINGS:
The impeller is mounted on pillow block bearings. One is a
locating bearing while the other is a non – locating (FREE) bearing. The
bearings are spherical roller type housed in bearing housing. Or the
bearings are of sleeve types that are selected based on the contractual
requirement and or on the basis of the selection requirement.
5. DAMPER ASSEMBLY:
This consists of a single piece casing, damper flaps, damper
bearings and the actuating mechanism. It is welded casing flanged at both
the ends. The bearing pedestals are mounted to the sidewalls by screws.
There are 3 to 5 flaps fixed by screws on to their shafts, which
are supported by pedestals providing dry lubrication. The flat shafts carry
clamping levers and feather keys transmit the adjusting torque and a
linkage connects the individual clamping levers.
6. SEALS:
The sealing for the shaft with the spiral casing consists of a
labyrinth section For axial and asbestos strip for radial sealing. The
asbestos strip ensures that the movement of the spiral casing during hot
conditions relative to the impeller wheel does not attack the fan’s
functioning. The unmachined flanges of the spiral casing are sealed with
asbestos rope.
1.8 Methods to drive the Fan
Various methods are used to the Fan
Prime movers
Electric motors (the most commonly used)
Engines
Turbines (compressed air to steam)
Compressed air jets.
1.8.1Types of motor drives
There are three ways that can be used for an electric motor to drive a Fan:
1. Belt drive
2. Direct drive
3. Gear drive
1.8.2 Types of Electric motors used to drive fans:
1. Three-phase squirrel-cage motors
2. Three-phase wounded-rotor motors
3. Single-phase, single phase induction motors
4. Single-phase, permanent-split-capacitor motors
5. Single-phase, shaded-pole motors
6. Single-phase universal motors
7. Single-phase, inside-out induction motors
1.9 FAN SPECIFICATIONS:
Backward Aerofoil Bladed Fan Application- Primary Air Fan Power- 1500 KW Plant Capacity- 250 MW Fan size- NDZV 20 BAB2 Speed- 1000 rpm Head- 985 mmmw Pressure ~ 9850 Nm/Kg Volume – 50 m3/s Material Used – Naxtra 70
CHAPTER 2
LITERATURE REVIEW
CHAPTER 2
LITERATURE REVIEW
FINITE ELEMENT ANALYSIS (FEA) :
2.1 Introduction:
Finite Element Analysis (FEA) is a computer-based numerical
technique for calculating the strength and behavior of engineering structures.
It can be used to calculate deflection, stress, vibration, buckling behavior
and many other phenomena. It can be used to analyze either small or large-
scale deflection under loading or applied displacement. It can analyze elastic
deformation, or "permanently bent out of shape" i.e., plastic deformation.
Computer is required because of the astronomical number of calculations
needed to analyze a large structure. The power and low cost of modern
computers has made Finite Element Analysis available to many disciplines
and companies.
2.2 Historical Background:
The very basics of the finite element method rose from the
advances in aircraft. It all began with Hrenikoff, in 1941 presenting a
solution to elasticity problems using “the frame work method”. This trend
continued with Courant’s paper based on piecewise polynomial interpolation
in 1943. Turner et al. derived stiffness matrices for truss, beam and other
elements and presented their findings in 1956. But Clough first coined the
term finite element in 1960.
2.3 What is FEA?
The finite element analysis is a kind of analysis in which a
complex region defining a continuum is discretized into simple geometric
shapes called finite elements. The material properties and the governing
relations are imposed on these elements and expressed in terms of unknown
values at element corners.
An assembly process duly considering the loading and
constraints, results in a set of equations. Solution to these equations gives us
the approximate behavior of the continuum.
2.4 Need for Finite Element Analysis:
Finite Element Analysis makes it possible to evaluate a detailed
and complex structure, in a computer, during the planning of the structure.
The demonstration in the computer of the adequate strength of the structure
and the possibility of improving the design during planning can justify the
cost of this analysis work. FEA has also been known to increase the rating of
structures that were significantly over designed and built many decades ago.
In the absence of Finite Element Analysis (or other numerical
analysis), development of structures must be based on hand calculations
only. For complex structures, the simplifying assumptions required to make
any calculations possible can lead to a conservative and heavy design. A
considerable factor of ignorance can remain as to whether the structure will
be adequate for all design loads. Significant changes in designs involve risk.
Designs will require prototypes to be built and field-tested. The field tests
may involve expensive strain gauging to evaluate strength and deformation.
With Finite Element Analysis, the weight of a design can be
minimized, and there can be a reduction in the number of prototypes built.
Field-testing will be used to establish loading on structures, which can be
used to do future design improvements via Finite Element Analysis.
2.5 The Finite Element Method:
In general, in the finite element method, a structure is broken
down into many small simple blocks or elements. The behavior of an
individual element can be described with a relatively simple set of equations.
However, there are two general approaches associated with the
finite element method. One approach called the force method uses the
internal forces as the unknown constraints of the problem, while the other,
the displacement method (or) stiffness method uses displacement as the
unknown.
In the finite element method the continuum is discretized into
small inter connected elements called finite elements, and these elements
have a displacement function associated with it. Each inter connected
element is linked, directly (or) indirectly to every other element through
common interfaces including the nodes and boundary line and surfaces. By
using the known stress strain properties of the material making up the
structure, one can determine the behavior of a given node in terms of
properties of every other in the structure. The total set of equations
describing the behavior of each node results in a series of algebraic
equations best expressed in matrix notation.
2.6 Concepts of FEA:
As described earlier the FEA can be used to determine the
stress and deflection of any structure under load.
According to Newton’s II law,
The force on any body due to external load is given by,
F = ma
This under equilibrium conditions the above equation can be represented in
the differential form as,
mä + cå + ka = 0
where,
a = kx
å = dx/dt
ä = d2x/dt2
So,
[m. (d2x/dt2)] + [c. (dx/dt)] + kx = 0
In matrix form is represented as,
[m] * [k] * [δ] = [f]
By solving the above matrix equations with the values given
(or) solved the values for stress and deflection can be determined easily.
2.7 General procedure for FEA:
With the advent of hi-tech computers, the FEA solutions for complex problems are made easy and simple. The general procedure for the FEA is outlined in the form of a flowchart as below:
FLOW CHART. 2.1
Pre – processor
Read the input data and identify the design constraints.Model the continuum.Identify the element type and mesh the model.Define the boundary conditions and load data.
Processor/solution
Compute element stiffness matrices.Assemble element equations.Solve equations for the conditionCompute results.
Pre – processor
Plot the resultsInterpret the results
27.1 Discretization:
It is the process by which a closed form mathematical
expression such as a function (or) a differential (or) integral equation
involving functions, all of which are viewed as having an infinite continuum
of values throughout some domain, is approximated by analogous
expressions that prescribes values at only a finite number of discrete points
(or) volumes in the domain.
2.7.2 Meshing:
A finite element model includes a mesh of nodes and
elements. The best way of creating mesh is to create the part’s geometry,
then generate a mesh on the geometry. Since the finite element model is
associated with the part, any change to the part is automatically reflected in
the nodes and elements of the mesh. Part geometry based meshes are also
used for geometry-based optimization.
There are generally two types of meshes;
1.MAPPED MESH:
It is a kind of mesh in which the points of the mesh are
arranged in a regular way all through the continuum and can be stretched to
fit a given geometry.
2.FREE MESH:
It is a kind of mesh where the points fill the space to be
considered but is not connected with the regular topology. The mesh with an
irregular structure is often referred to as an unstructured (or) free mesh.
FIG. 2.1
DIAGRAMATIC REPRESENTATION OF MAPPED AND FREE
MESH
FREE MESH
MAPPED MESH
2.8 Applications of FEA:
There are several engineering applications of FEA, but some of the notable one’s are mentioned below:
Structural analysis
Structural machines
Aerospace engineering
Solid mechanics and foundation engineering
Rock mechanics and heat conduction
Hydrodynamics and hydraulic engineering
Water resources and nuclear engineering.
2.9 Setting element attributes:
Before generating a mesh of nodes and elements, the element
attributes are to be defined.
Element type
Real constant set
Material Properties set
Element co-ordinate system
2.10 Boundary conditions:
2.10.1 Definition of Boundary condition
Boundary conditions are nothing but the constraints of the model
that is to be analyzed. The constraints may be displacement, inertias, loads
(forces, moments), temperature, fluid velocity, etc., for every model the
boundary conditions are must be specified. Without the impositions of the
boundary conditions, the element and assemblage stiffness matrices, [k] and
[k], are singular; that is, their determinants vanish and their inverse do not
exist.
The physical significance of this is that a loaded body or structure
is free to experience unlimited rigid body motion unless some supports or
kinematic constraints are imposed that will ensure the equilibrium of the
loads. These constraints are the boundary conditions.
2.10.2 Boundary conditions for the model
1.Displacement:
The rotating motor shaft is fixed in the impeller therefore the
displacement on the impeller hole is zero in all degree of freedom.
2.Angular velocity and angular acceleration:
The impeller rotates about the “z” axis at a speed of
1000rpm. Therefore
Angular velocity = (2πN)/60
= 104.7 rad/sec
The angular acceleration is also given as 9810 rad/sec2.
2.11 Material properties:
Once a mesh has been built to describe the domain occupied by
the structure, the rest of the computer model can be built. It is only at this
stage that the description of the physical problem generated in the initial
stage of the analysis process can be related to the computational geometry
described by the mesh of nodes and elements. For each element, its material
properties must be defined together with the boundary conditions on the
faces of the elements, or at the nodes, which form the exterior of the mesh.
It is not necessarily straight forward task to define precisely the
material properties and, frequently, they must be approximated when
compiling the model data for an analysis.
For this model, the constant Isotropic material has been used and
their values are
1.Young’s modulus EX = 21000 kg/mm2
2. Density DENS = 8.002 e-10 mN/mm3
3. Poisson’s ratio NUXY = 0.3
2.12 Element type
Element type used in FEA may be described in terms of their
shape (through the relative positions of its nodes) and degrees of freedom
(possible directions of movements of each node). The element plot and
nodal plot for the model are shown in fig.
ELEMENT PICTORIAL VIEW TYPE
2-NODED BEAM ELEMENT
1 - D
3 – NODED BEAM ELEMENT
1 – D
3 – NODED TRIANGULAR ELEMENT
2 – D
6 – NODED TRIANGULAR
ELEMENT
2 – D
4 – NODED AREA ELEMENT
2 – D
8 - NODED AREA ELEMENT 2 – D
8 – NODED BRICK ELEMENT 3 – D
4 –NODED PYRAMID ELEMENT
3 – D
TABLE 2.1
ELEMENT TABLE
2.12.1 Element type for the model
For this analysis 4-noded area element (SHELL 63) is used.
SHELL 63 element is well suited for mapped meshing for this model.
Usually for any area of a model can be meshed using 4-noded area element
(SHELL 63) in a uniform manner (mapped meshing). It is a kind of mesh in
which the points of the mesh are arranged in a regular way all through the
continuum and can be stretched to fit a given geometry so that the results
will be more accurate when compared to free mesh results.
2.12.2 Choosing the element type
1.The range of elements and testing the elements:
It is not possible to present a set of universal guidelines to
develop any finite element model as such structural problem and element
type have their own particular features. It is not even possible to give rules
for what appears in packages to be identical element types since their
formulation can be different.
Any test for element behavior should be more complicated than
the situation of a simple rectangular geometry with a constant load, since
simple situations can give a false impression of the convergence
characteristics for realistic problems.
Quadratic elements, be they membrane or solid elements, give
the best compromise between accuracy and efficiency for general use.
When modeling a structural problem that can be classified, as
having bending deformation and the geometry is either flat or curved, then
the preferred choice of elements is always the general shell element.
Curved surfaces should not be modeled using flat elements as the
discontinuity at element boundaries introduces significant error.
2. Using a Hierarchy of elements:
Analysts should develop a model using a step by step approach.
This means that they should start with a simple approximation, say a beam
model, and make it more precise as the finite element modeling progresses.
Never tackle a real problem directly as this is likely to be time consuming
and wasteful of resources. Remember, that more results that are generated
the more effort that will be necessary to check that they are reliable and
relevant.
3. Restricting the dimensions of a problem:
Avoid the use of solid elements to model a problem where the
length in one of the spatial dimensions, for example the material thickness,
is much less than the lengths in the other two dimension.
4. Plate and shell elements:
Plate and shell elements have historically been the most difficult
to use in terms of achieving reliable and cost effective solutions. In
particular these elements in a static analysis do not give an acceptable
solution if the displacement of the nodes normal to the surface of the
material is greater than the thickness of the material.
5. The role of compatibility:
Elements must have the same order, all though one can mix three
sided and four sided elements.
There must be connection between the corner nodes of
neighboring elements and, if present, continuity between the edge nodes of
adjacent elements.
6. Elements of model contact:
Before developing a three dimensioning model for a problem
with contact between different parts, check that the package has three
dimensional contact algorithms.
2.13 Fan laws and Efficiency
2.13.1 Fan laws:
There are certain fan laws that are used to convert the
performance of a fan from one set of variables to another.
1.Conversation of fan performance
Suppose a fan of a certain size and speed has been tested and its
performance has been plotted for the standard air density. We then can
compute the performance of a fan of geometric similarity by converting the
performance data in accordance with these fan laws without running a test
on the other fan. It called as general fan laws.
2.Variation in fan speed
In order to convert the performance of a fan at one speed to
another speed, We take a number of points on the performance graph and
convert the corresponding data for air volume, static pressure, bhp,
efficiency and noise level fro the speed of the graph to the desired speed
using the following rules.
The air volume (cmf) varies directly with the speed
(cfm2/cfm1) = (rpm2/rpm1)
The pressure vary as the square of the speed
(Sp2/Sp1) = (rpm2/rpm1)
The brake horse power varies as the cube of the speed
(bhp2/bhp1) = (rpm2/rpm1)
The efficiency remains constant but, of course, shifts to the new air
volume values.
Variation in fan size
This law is used to convert the performance of one fan to
another fan when they are geometrically similar .
The fan laws for size , however , can be used only if the two
fans are in geometric proportion .
Both fans have the same number of blades .
Both fans have the same blade angles and any other angles on
the fan wheel and fan housing.
If the diameters of the two wheels are D1 and D2 for a size
ratio D2/D1, all other corresponding dimensions of wheel and housing have
the same ratio.
The air volume (cfm) varies has cube of the size. (cfm2/cfm1)
= (D2/D1)3
The pressure vary as the square of the size .
(sp2/sp1) = (D2/D1)2
The bhp varies as the fifth power of the size .
(bhp2/bhp1) = (D2/D1)5
Variation both fan size and fan speed
If both the fan size D and the fan speed (rpm) are varied , the
two sets of rules discussed above can be applied consecutively , in either
sequence .
(cfm2/cfm1) = (D2/D1)3 *(rpm2/rpm1)
(sp2/sp1) = (D2/D1)2 *(rpm2/rpm1)2
(bhp2/bhp1) = (D2/D1)5 *(rpm2/rpm1)3
(ME2/ME1)=1
Variation in Density
This fan law is used when the fan operates at high altitude
where the air density is less , where the fan handles hot or cold air (the air
density is inversely proportional to the absolute temperature) , or where the
fan handles a gas other than air , while the size and speed of the fan remains
constant.
The air volume remains constant
(cfm2/cfm1) = 1
The pressure vary directly as the density ρ
(sp2/sp1) = (ρ2/ρ 1)
The bhp varies directly as the density ρ
(bhp2/bhp1) = (ρ2/ρ 1)
The efficiency remains constant
2.13.2 Fan Efficiency
Fan work can be equated to the system resistance. Fan pressure has
the dimension of work per unit volume. Thus the system resistance may also
be regarded as the work required per unit volume of gas.
Power kw = Q X Ps
Work = force X Distance
Power = force X Velocity
= pressure X Area X Velocity
= pressure X Volume
The ratio of this air power to the power required to drive the fan is
the fan efficiency. The pressure may be total (including the velocity
pressure) or static and resulting efficiencies may also be “total” or “static”.
Selecting a fan of higher efficiency normally results in higher first
cost, but in lower operating cost.
1. Size and type limitations to good efficiency
High operational efficiencies are only achievable with certain types
and sizes of fan; indeed, the definition of “good” and “high” efficiency
depends on the class and quality of the fan being considered.
For a particular type of fan the best efficiencie swill be achieved by
higher specific speed fans of backward curved, backward inclined or aerofoil
bladed design with the fans being medium or large diameter and operating at
Reynolds numbers in excess of 20x105.
Where Reynolds number = (ρuD) / μ
D – Fan dameter
ρ – Fluid density
μ – Dynamic viscosity
2. Specification of fan requirements
Aerodynamic duty:
An important factor in ensuring a successful fan system is the correct
specification of the fan. The starting point in the specification of the fan is
knowledge of flow rate, which the fan (or fans) is required to handle. Often
there will be a range of flow rates over which the fan will be required to
operate and if this range is large it may be necessary to consider employing a
number of fans in parallel.
The next parameter to be defined is the pressure rise required of the
fan to move the gas through the system. This requires a knowledge of the
layout the system including pipe lengths, pipe diameters and elevations, a
knowledge of all the pipe work components in the system and information
on the properties of the gas being moved, particularly its density and
viscosity. From this it is possible to calculate the pressure losses in the
system.
If the fan duty varies with time then the use of variable geometry or
variable speed is almost certainly economically beneficial in terms of whole
life costs, if the duties of the fan are anticipated to increase with the time e.g.
: - if the output of the process system in which the fan operates is expected
to grow, then it may be possible to commence operation with a reduced
diameter (or reduced width) impeller fitted in to a standard casing and, as the
demand increases, fit the standard impeller. this will generally be preferable
to initially running the fan at a flow rate way below its design condition and
offer advantages of reduced power consumption and reduced bearing loads.
3. Estimation of fan type, size and speed:
Once the flow rate and pressure are known it is possible to derive
some idea of feasible options for the type of fan required. Simple formula
will allow initial estimates to be made of the probable type(s) and size(s),
which are optimum for a particular installation.
The specific speed, Ns, of a fan is a measure of the fan shape or type.
Ns is defined as Ns = [w (Q) 0.5] / (gH) 0.75
Where w is the rotation speed of the fan (rad / sec)
Q is the volume flow rate (m3 / sec)
gH is the specific energy ( J / Kg )
gH = (p / ρ)
Where p is the fan pressure raise – pa
ρ is the fluid density – Kg / m3
Knowing Q and gH, a range of rotational speeds can be assumed.
Typically these will correspond to 2, 4, or 6 pole motor speeds with a wide
choice available for belt driven fans. The value of Ns defines the optimum
fan type for the duty. If Ns is less than about 1.5 the fan will be a centrifugal
machine; if Ns is greater than about 2.5 the optimum fan will be an axial,
between 1.5 and 2.5 the optimum unit would be mixed flow type.
The next stage is to determine the approximate impeller diameter. For
a centrifugal type fan the dia can be estimated from the relationship, Farrant
V2 tip = gH / (0.8 - 0.23 Ns)
And for an axial or mixed flow machine from
D = 2[ gHQ / w3kL ]0.2
Where the loading coefficient, kL, has a value typically in the range 0.01 to
0.08.
It is thus possible to get an idea of the potential speed and dia of the
fan best suited to the duty. If either the speed or dia appears impractical this
may well point to the need to consider multistage fans or a series of fans in
parallel.
For multistage fans the head per stage reduces, thus raising the
specific speed per stage. For fans in parallel the flow per fan decreases thus
increasing the specific speed per unit.
2.14 STRESS ANALYSIS
Stress is defined as "a force tending to produce strain or
tension and to change the form or dimension of a solid", by dictionary. A
common man's understanding of stress is very much different from that of an
engineer. For an engineer
Limit F
Stress = A 0
A
Where, F = Force vector acting on the small area
M
Ever since the invention of Hooks
Law by the famous English Scientist Robert Hook (1935 -1703) analysis of
stress and strain has attracted many brilliant scientific and engineering
minds. Today, the theory is well developed and is widely used. However, a
general analytical calculation for the state of stress and strain in a general
solid is not yet available and is considered impossible to obtain. ' Stress
analysis problems can be solved using two sets of methods, i.e. experimental
and theoretical Hence, many numerical techniques have been developed and
are widely used in the industries for stress analysis. Finite Element Method
(FEM), one of the numerical techniques, was developed in fifties. Today
Finite Element Method is very popular and widely used in industry. Though
the underlying concept was originally introduced by Argyris in 1954-55, it
was supplemented by Turner, Clough, Martin and Toop in 1956. The
method is widely used since the development of high-speed electronic
digital computers and development of numerical methods to handle difficult
mathematical problems. Though the method was originally developed as a
tool for structural analysis, the theory and formulation have been
progressively refined and generalized and the method has been successfully
applied to many other fields like thermal, fluid, vibration, electrostatics,
Electro-magnetism, etc.
2.14.1 NEED FOR STRESS ANALYSIS
After the Industrial Revolution of nineteenth century,
large and complex machines and structures were built to mankind. As the
time passed, new types of machines and structures were built in critical and
demanding applications, requiring high reliability and economy. These
factors in design, under new environment of competition resulted in
application of analytical methods in the solution of engineering problems.
Design is no longer based upon empirical formulae. The importance of
analytical methods combined with laboratory experiments in the solution of
engineering problems has been recognized and accepted by the engineering
community. The conflicting requirements of increased reliability, reduced
cost and improved performance make the task of designer extremely
complicated.Reduced cost means reduced weight. Increased reliability with
reduced weight can be" achieved only on the basis of careful analysis of
stress distribution in the structure and experimental investigation of the
mechanical properties of the materials. Experimental techniques have
become very refined over the years. Similarly, analytical techniques have
become complex and advanced, leading to better understanding of stress
distribution in complicated solids.
CHAPTER 3
INTRODUCTION TO ANSYS
CHAPTER 3
3.1 Introduction to ANSYS
ANSYS is a general purpose finite element computer program for
the solution of structural, heat transfer engineering analysis. ANSYS
solution to capabilities includes: static analysis, elastic, plastic, thermal,
stress, stress stiffened, large deflections, bilinear elements, dynamic
analysis, model, harmonic response, linear time history, non-linear time
history, heat transfer analysis: conduction, convection, radiation, coupled to
fluid flow, coupled to electric flow, structures, magnetics, etc. Analysis can
be made in one, two, or three dimensions, including axisymmetric and
harmonic element options. ANSYS also contains a complete graphics
package and extensive pre and post processing capabilities.
3.2 ANSYS offers
1.tensive capabilities
2.ailability
3.owth and development
4.pport
3.3 Examples of ANSYS analysis
Examples Special options used
1.Laying ocean cable Dynamic, stress stiffening, large
deflection, hydrodynamic forces.
2.Automatic crash studies Dynamic, large deflection, plasticity,
gaps.
3.Evaluation of golf club swing Large rotations, stress stiffening.
4.Railroad tank car Dynamic, Fluid elements, pressure
vessel fatigue evaluation.
5.Piping system evaluation Static, seismic, gaps, large
deflection.
6.Electric furnaces smelting Heat transfer, thermal- electric