Unit - 6
Applications of Computer Aided Engineering
Q1) Give computation of fluid dynamics.
A1)
Computational Fluid Dynamics:
Computational fluid dynamics (CFD) is a department of fluid mechanics that makes use of numerical evaluation and records systems to research and resolve issues that contain fluid flows.
With high-pace supercomputers, higher answers may be achieved, and are regularly required to resolve the biggest and maximum complicated issues. Ongoing studies yields software program that improves the accuracy and pace of complicated simulation situations which include transonic or turbulent flows.
Q2) What are three dimensions of fluid dynamics?
A2)
Three Dimensions of fluid dynamics:
Initial validation of such software program is generally carried out the use of experimental equipment which include wind tunnels. In addition, formerly carried out analytical or empirical evaluation of a selected hassle may be used for comparison.
A very last validation is regularly carried out the use of full-scale testing, which include flight tests. CFD is implemented to a huge variety of studies and engineering issues in lots of fields of observe and industries, together with aerodynamics and aerospace evaluation, climate simulation, herbal technological know-how and environmental engineering, commercial device layout and evaluation, organic engineering, fluid flows and warmth transfer, engine and combustion evaluation, and visible consequences for movie and games.
In physics and engineering, fluid dynamics is a sub discipline of fluid mechanics that describes the float of fluids—drinks and gases. It has numerous sub disciplines, such as aerodynamics (the have a look at of air and different gases in motion) and hydrodynamics (the have a look at of drinks in motion). Fluid dynamics has a huge variety of applications, such as calculating forces and moments on aircraft, figuring out the mass float charge of petroleum thru pipelines, predicting climate patterns, know-how nebulae in interstellar area and modelling fission weapon detonation. Fluid dynamics gives a scientific structure—which underlies those realistic disciplines—that embraces empirical and semi-empirical legal guidelines derived from float size and used to clear up realistic problems.
Before the 20th century, hydrodynamics changed into synonymous with fluid dynamics. This remains contemplated in names of a few fluid dynamics topics, like magneto hydrodynamics and hydrodynamic stability, each of which also can be implemented to gases.
Q3) What is translation of fluid?
A3)
Translation of a Fluid Element
The motion of a fluid detail in area has 3 awesome capabilities simultaneously. Translation Rate of deformation Rotation. Figure suggests the photo of a natural translation in absence of rotation and deformation of a fluid detail in a two-dimensional float defined with the aid of using a square Cartesian coordinate system.
In absence of deformation and rotation,
a) There might be no alternate with inside the period of the edges of the fluid detail.
b) There might be no alternate with inside the covered angles made with the aid of using the edges of the fluid detail.
c) The facets are displaced in parallel direction.
This is feasible whilst the float velocities u (the x element velocity) and v (the y element velocity) are neither a characteristic of x nor of y, i.e., the float area is definitely uniform.
If an aspect of go with the drift pace will become the characteristic of best one area coordinate alongside which that pace aspect is defined.
For example, if u = u(x) and v = v(y), the fluid detail ABCD suffers a extrude in its linear dimensions together with translation there may be no extrude with inside the blanketed attitude via way of means of the perimeters as proven in Fig.
Q4) What is existence of flow?
A4)
Existence of Flow
- A fluid need to obey the regulation of conservation of mass in route of its glide as it's miles a fabric body.
- For a Velocity subject to exist in a fluid continuum, the speed additives need to obey the mass conservation precept.
- Velocity additives which comply with the mass conservation precept are stated to represent a likely fluid glide Velocity additives violating this precept, are stated to explain a not possible glide.
- The lifestyles of a bodily viable glide subject is confirmed from the precept of conservation of mass.
- The particular dialogue on that is deferred to the following bankruptcy in conjunction with the dialogue on ideas of conservation of momentum and energy.
Q5) Give equilibrium equation of fluid.
A5)
Equilibrium equations of fluid:
A fluid can help no shearing strain whilst in equilibrium. The strain for compression is truly the stress. If there aren't any any outside forces (consisting of gravity), the stress is the equal anywhere with inside the fluid whilst the fluid is in equilibrium.
Fluid statics or hydrostatics is the department of fluid mechanics that research the circumstance of the equilibrium of a floating frame and submerged frame "fluids at hydrostatic equilibrium and the strain in a fluid, or exerted through a fluid, on an immersed frame".
It is likewise applicable to geophysics and astrophysics (for example, in know-how plate tectonics and the anomalies of the Earth's gravitational field), to meteorology, to medicine (with inside the context of blood strain), and plenty of different fields. Hydrostatics gives bodily causes for lots phenomena of ordinary life, along with why atmospheric strain adjustments with altitude, why wooden and oil flow on water, and why the floor of nonetheless water is constantly level.
Q6) What is gravity on fluid?
A6)
Gravity on fluids
When handling a fluid, we now not have factor masses. Forces consisting of gravity act on fluid factors that are similar to quantity factors. This results in the concept of a frame pressure (pressure according to quantity). For gravity, this becomes:
f = ρg = -ρgy , where ρ is the mass per volume, ρ = dm/dV.
Newton’s 2nd law becomes (with P being the pressure):
Fx = +Pleft dAleft - Pright dAright = 0
Fz = +Pin dAin – Pout dAout = 0
Fy = +Pbottom dAbottom – Ptop dAtop -ρg dV = 0 .
The volume element can be written as:
DV = dx dy dz = dAxz dy , so that, with dAtop = dAbottom = dAxz, we have
Pbottom – Ptop = ρg Δy .
This can be generalized for a body force to be:
P2 – P1 = ΔP = r1r2 f • dr , or f = P .
Note that the constant pressure lines (actually surfaces) are perpendicular to the body force, f. Also, since P = 0, we have f = 0, which allows us to have:
P(r) – Po = ror f dr which is similar to a potential energy.
Q7) What is bulk modulus?
A7)
Bulk Modulus
The Bulk Modulus, B, is described as: B = pressure/ stress, in which pressure is clearly the pressure, P; and stress is ΔV/V : B = PV/ΔV, so we have -dV/V = dP/B. The minus signal comes from changing the ΔV right into a dV, however noting that the ΔV is a lower with inside the volume, now no longer an increase. Let’s now bear in mind density, ρ = m/V. The amount dρ is
dρ = d(m/V) = m d(1/V) = m {d(1/V)/dV} dV = m (-1/V2) dV,
So that the quantity dρ/ρ becomes:
dρ/ρ = m (-1/V2) dV / (m/V) = -dV/V .
Note that whenever dV increases, dρ decreases, and
When dV decreases, dρ increases. Hence the difference in the sign.
Putting -dV/V = dP/B together with dρ/ρ = -dV/V gives:
dρ/ρ = dP/B,
And integrating both sides gives:
Ln [ρ/ρo] = PoP (1/B) dP, or
ρ = ρo exp [PoP (1/B) dP ]
Q8) Explain four special cases in detail.
A8)
Four special cases
Case 1: incompressible fluid
When we have incompressible fluid (B ≈ ∞), then ρ ≈ constant, so using Pbottom – Ptop = ρg Δy we have:
Pbottom = Ptop + ρgh , where h = height (or depth) of the fluid.
Case 2: Bulk modulus is constant
Here we consider the case where the bulk modulus is a constant, independent of pressure and density. In this case, the density equation gives:
ρ = ρo exp [PoP (1/B) dP ] = ρo exp [P/B – Po/B] .
The pressure equation gives us:
Pbottom – Ptop = ρg Δy , or
DP = ρg dy = ρo exp{P/B – Po/B} g dy = ρo eP/B e-Po/B g dy.
We can separate this equation to get:
e-P/B dP = ρo e-Po/B g dy , or
PoP e-P/B dP = yo y ρo e-Po/B g dy
And with yo = 0 (measured from the surface) and Po = atmospheric pressure (at the surface), we have upon integration:
(-B) e-P/B – (-B)e-Po./B = ρo e-Po/B g y
Case 3: Ideal gas at constant Temperature
For an ideal gas, we have the ideal gas law:
PV = nRT
Where n is the number of moles, R is the gas constant (R = 8.3 J/mole-K), and T is the temperature (in an absolute scale such as Kelvin). This relates the volume to the pressure, and hence the density to the pressure:
ρ = m/V = m / {nRT/P} = Pm/nRT .
The m is the mass, and n is the number of moles. We can combine these two to get the mass per mole, M = m/n, so the
ρ = PM/RT
We can now use this in the relation for pressure:
DP = ρg dy = (PM/RT)g dy .
This can be separated and integrated to give:
PoP (1/P)dP = yo y (Mg/RT) dy, or
Ln {P/Po} = Mgy/RT , or P = Po e(Mg/RT)y
The above has y as the “depth” where P increases. To make it into a height (where P decreases), we must put in a negative sign for the y:
P = Po e-(Mg/RT)y
Q9) Give conversations form of fluid flow equation.
A9)
Conservation shape or Eulerian shape refers to an association of an equation or machine of equations, typically representing a hyperbolic machine, that emphasizes that a belongings represented is conserved, i.e. a sort of continuity equation.
Conservative shape has an advantage: its fundamental shape permits discontinuous solutions (main to Rankine-Hugoniot relation and accurate surprise speed). Non-conservative shape does now no longer have one of these character (it permits best easy differentiable solutions).
Discrete conservation is essential in computing shocks. If conservation is violated, a surprise may also journey at an incorrect speed. Successful non-conservative schemes may also flip out to meet a few shape of discrete conservation.
Rather than conservation itself, its miles extra essential to apply a proper conservation shape (want to select out proper portions that ought to be conserved) considering that a incorrect conservation shape can result in an incorrect surprise speed.
Conservative equation is primarily based totally at the precept of conservation of mass. It states, “When a fluid flowing eleven though the pipe at any section, the amount of fluid in line with 2d stays constant”.
Consider a fluid element of lengths dx, dy, dz in the direction of x, y, z.
Let u, v, w are the inlet velocity components in x,y,z direction respectively.
Let ρ is mass density of fluid element at particular instate.
Mass of fluid entering the face ABCD (In flow)
= Mass density x Velocity x-direction x area of ABCD
= ρ x u x (∂y x ∂z)
Then mass of fluid leaving the face EFGH (out flow) = (ρu∂y . ∂z) + ∂ / ∂x (ρu∂y∂z)
Rate of increases in mass x-direction = Outflow – Inflow
= [ (ρudydx) + ∂ / ∂x (ρudydz) dx ] - (ρudydz)
Rate of increases in mass x direction = ∂ / ∂x ρ u dx dy dz
Similarly,
Rate of increase in mass y-direction = ∂ / ∂y ρ v ∂x ∂y ∂z
Rate of increases in mass z-direction = ∂ / ∂z ρ w ∂x ∂y ∂z
Total rate of increases in mass = (7.7.3) + (7.7.4) + (7.7.5)
= ∂x ∂y ∂z [ ∂ρu / ∂x + ∂ρv / ∂y + ∂ρw / ∂z ]
By law of conservation of mass, there is no accumulation of mass, and hence the above quantity must be zero.
∂x. ∂y. ∂z [ ∂ρu / ∂x + ∂ρv / ∂y + ∂ρw / ∂z ] = 0
∂ (ρu) / ∂x +∂ (ρv) / ∂y + ∂ (ρw) / ∂z = 0........for compressible fluid
If fluid is incompressible, then is constant
∂u / ∂x + ∂v / ∂y + ∂w / ∂z = 0
This is the continuity equation for three-dimensional flow.
NOW, for tow-dimensional flow, the velocity component w = 0
Hence continuity equation is, ∂u / ∂x + ∂v / ∂y = 0
Q10) What are integral form of the conservation laws?
A10)
Integral form of the conservation laws:
- The essential shape of the overall equations is a macroscopic assertion of the concepts of conservation of mass and momentum for what's referred to as a manipulate quantity. A manipulate quantity is a conceptual tool for in reality describing the diverse fluxes and forces in open-channel float. A conceptual manipulate quantity for open-channel float is proven in determine 9.
- The downstream face of the manipulate quantity at station Equation is also assumed to be orthogonal to the float course. The aspects and backside of the manipulate quantity are fashioned via way of means of the edges and backside of the channel.
- The pinnacle of the manipulate quantity is fashioned via way of means of the water surface. The period of the manipulate quantity, Equation , does now no longer need to be small and is measured alongside the space axis described previously.
- The essential shape of the equations may be defined clearly in a 1-D approximation; therefore, the equations are offered right here without derivation, accompanied via way of means of dialogue of what every principal time period or set of phrases represents with inside the conservation principle.
- To preserve the information as easy as possible, the burden coefficients used to accurate sure integrands with inside the essential shape for the results of curvilinear float are neglected at first. These weights are delivered later while the overall shape of the equations is advanced for curvilinear channel alignments.
Q11) What is conservation of mass?
A11)
Conservation of Mass
The conservation of mass principle for a control volume is
The time c language of integration is described via way of means of factors in time, Equation and Equation, such that Equation. (The means of the subscripts on those time factors is defined in greater element in next sections.)
The time period I(t) denotes the influx of water that enters the manipulate quantity over or thru the perimeters of the channel. Density is consistent and isn't proven in equation 27 due to the fact every time period might have a consistent multiplier that cancels from the relation.
Thus, the conservation of mass is equal to conservation of water quantity in FEQ simulation. Equation 27 is a unique mathematical assertion of an easy concept. The left-hand facet of equation 27 is the alternate in quantity of water contained with inside the manipulate quantity at some stage in the time c language Equation.
The quintessential of waft place with admire to distance at a hard and fast time defines the quantity of water with inside the manipulate quantity at that point. The right-hand facet of equation 27 is the internet quantity of influx to the manipulate quantity (influx minus outflow) at some stage in the time c language.
Water enters from upstream, Equation, leaves downstream, Equation, and enters over or thru the perimeters of the channel, I(t). Thus, equation 27 suggests that the alternate in quantity of the water with inside the manipulate quantity at some stage in any time c language is same to the distinction among the quantity of influx and the quantity of outflow at some stage in that point c language.
The time period I(t) represents what's typically referred to as the lateral influx, which comes from numerous sources: runoff from the land surface, discharges from sewers, outflows of water from pumping, and others. If the lateral waft is out of the channel, then I(t) is negative.
Q12) What do you mean by conservation of momentum?
A12)
The precept of conservation of water quantity consists of best the flows and modifications in volumes. The conservation of momentum consists of the momentum flux and numerous forces at the obstacles of the manipulate quantity.
As mentioned previously, initial proof from laboratory research suggests that the vector nature of momentum does now no longer notably have an effect on 1-D flows; therefore, glide is dealt with as though it had been all with inside the identical path.
Impulse is a time essential of a force. In maximum fundamental fluid mechanics texts (for example, Streeter and Wylie 1985, p. 117), the conservation of momentum for a manipulate quantity in a single dimension, x, is expressed as (28)
Where
The cowcatcher set up on the underframe of electrical a couple of units (EMU) is able to cleansing up boundaries from the tune and easing influences in crashing. During its long time of operation, fatigue failure subjected to alternating hundreds is the primary failure mode of EMU factor failure
Thus, cyclic operation of the cowcatcher is clearly a fatigue harm accumulation process. When the buildup harm reaches a crucial value, the cowcatcher fatigue occurs. Therefore, its miles of significance to assess and verify the reliability and fatigue sturdiness of the cowcatcher. Cowcatcher is a essential factor to comb away the boundaries and take in kinetic power.
Some researches on cowcatcher had been conducted. Ding and Zhao2 followed a brand new power soaking up shape and filling fabric with the software of collision-resistant gadget layout primarily based totally on LS-DYNA simulation. They indicated that the brand new sort of cowcatcher optimization scheme is to be had for soaking up power and easing collision.
Also, whilst designing the cowcatcher, it's miles vital to pay interest now no longer most effective to the fundamental circumstance parameters, such as its shape, top and static electricity, however additionally to its power absorption overall performance to satisfy the safety necessities for easing the influences.
To enhance the provider existence and make sure the protection at the same time as cars are in motion, it's miles vital to take the fatigue sturdiness into in addition consideration. Three Shen et al. Four supplied a suggestion to evaluate fatigue sturdiness of automobile exhaust gadget the use of finite element (FE) simulations.
- Fatigue electricity is the very best strain that a fabric can resist for a given range of cycles without breaking.
- Fatigue electricity is tormented by environmental factors, consisting of corrosion.
- The most strain that may be carried out for a positive range of cycles without fracture is the fatigue electricity.
- The range of cycles that a steel can bear earlier than it breaks is a complicated feature of:
- Static and cyclic strain values.
- Alloy.
- Heat-remedy and floor circumstance of the material.
- Hardness profile of the material.
- Impurities with inside the material.
Fatigue electricity is used to explain the amplitude (or range) of cyclic strain that may be implemented to the cloth without inflicting fatigue failure, or the best strain that a cloth can face up to for a given wide variety of cycles without breaking.
The trendy fatigue electricity for copper alloys is that pronounced for 100,000,000 cycles.
At stresses above this fatigue electricity, fewer cycles may be carried out earlier than failure; at decrease stresses, the metallic will face up to greater cycles earlier than failure.
For example, ferrous alloys and titanium alloys have a awesome restriction, underneath which there seems to be no wide variety of cycles so one can purpose failure.
Other structural metals which include aluminum and copper do now no longer have an awesome restriction and could subsequently fail even from small strain amplitudes.
Fatigue electricity is as essential to the layout of elements with excessive deflection cycles, as yield electricity is to the fashion dressmaker who need to reap considered necessary touch forces.
Orientation influences the fatigue electricity.
Data normally compiled and posted are for check specimens with a longitudinal orientation (their period is parallel to the rolling direction).
But fatigue electricity may be measurably stricken by the way wherein the component is located at the strip for stamping.