# 3. turbine with a generator of size of a

3.
OBJECTIVE:

·
We
have come across with an idea of generating power in a traditional way and
utilizing that energy for an efficient mode of transportation.

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·
The
automobile industry is emerging in manufacturing electric cars by utilizing few
components of electric devices such as 3phase induction motor, inverter and the
power house which can be regular lithium ion batteries as in the case for tesla
motors or modified battery packs as in Nissan leaf.

·
These
electric cars having plenty of space because of un presence of IC engines which

·
Our
main objective is to install either the vortex bladeless concept or a small
wind turbine with a generator of size of a normal household use in the empty
space of those electric cars in the front portion.

·
Both
the wind turbine concept and the vortex bladeless concept starts at the moment
when the free stream air or the head wind strikes the blades in case of wind
turbine or when the air enters into the conduit in the case of vortex bladeless
concept.

·
Design
of the front portion should be in such a way that the head wind hits the blades
or enters into the conduit with a uniform flow in order to avoid the vibration
and mechanical damages of the system.

Fig : https://electrek.co/guides/tesla-model-s

METHODOLOGY :

As we discussed earlier
our objective is to install a small scale turbine which eventually becomes
power producing source for the prospective vehicle. The size (diameter) and the
corresponding desired power output are the main concern for our project. Let’s
take the example, the Tesla model S: It has the battery pack of 100kwh and runs
approximately 500-510km that shows the vehicle consuming 20kwh for every 100km
approximately. Let’s estimate the scale of the turbine which can increase the
range of the considered vehicle and we will see how much the increment in range
at different speeds by generating the power.

Let’s say,

Diameter of the rotor D
=0.50m

Mechanical efficiency ?m =0.9

Electrical efficiency ?e =0.95

Considering the free
stream velocity or head wind in this case is at 60kmph.
Considering the
velocity losses at the intake let’s consider the speed reduced to (V) 40kmph or
11.2m/s.

Power output  P = (power contained in wind * power
coefficient*mechanical efficiency*electrical efficiency)

P=P0*Cp*?m*?e  ……..(a)

Where

P0=1/2*?*A*V3

Substitute P0 in equation (a), we get

P=1/8*?*?*D2*V3* Cp* ?m* ?e

Cp=0.2
(least value considered)

P=1/8*1.22* ?*0.52*11.23*0.2*0.9*0.95

P=28.77W

This is the output
power generated by the wind turbine with the rotor diameter meter 0.5m. At the
speed of 11.2m/s the wind turbine generating the power of 28.77W or 28.77ws in
terms of energy, which concludes that if vehicle runs for 1 hour at 11.2m/s
speed the turbine can be able to produce 100kwh. This is the capacity of main
battery pack which in turn shows that the vehicle can run again for 500km
(assuming that vehicle runs at constant speed 11.2m/s).

If Cp is
taken as 0.1 the generating output will become

P=1/8*1.22* ?*0.52*11.23*0.1*0.9*0.95

P=14.39 W

For Cp=0.1, 14.39
W power or 14.39W-S energy generated at 11.2m/s. For 1 hour the turbine can be
able to produce

E=14.39*3 600

E=51.804 KWH

With
the 51KWH the vehicle can run for another 250km.The power generated would be AC
and it can be directly connect to the induction motor which drives the drive
wheel or for charging the battery pack which is our main concern.

Apart
from the output power there are certain parameters which should be consider for
the effective energy extraction while working under different conditions such
as turbulence in the wind, stresses and bending forces and other load forces.
Some of the turbulence models for calculating the turbulence are discussed
below:

Stochastic
turbulence models:

The following stochastic turbulence models
may be used for design load calculations. The turbulent velocity fluctuations
are assumed to be

a random vector field whose components
have zero-mean Gaussian statistics. The power spectral densities describing the
components are given in terms of the Kaimal spectral and exponential coherency
model or by the Von Karman isotropic model.

Kaimal spectral
model

The component power spectral densities are
given in non-dimensional form by the equation:

where

f is the frequency in
Hertz;

k is the index referring to
the velocity component direction (i.e. 1 = longitudinal, 2 =lateral, and 3 =
vertical);

Sk the single-sided velocity
component spectrum;

? kis
the velocity component standard deviation (see Equation (C.2)); and

Lk is the velocity
component integral scale parameter.

and
with

C.2 Exponential coherency model

The
following exponential coherency model may be used in conjunction with the
Kaimal autospectrum model to account for the spatial correlation structure of
the longitudinal velocity component:

where

Coh(r,f) is the coherency function defined by the complex magnitude of the
cross spectral density of the longitudinal wind velocity components at two
spatially separated points divided by the autospectrum function;

r is the magnitude of the projection of the separation vector between
the two

points
on to a plane normal to the average wind direction;

f is the frequency in Hertz; and

Lc = 3,5?1 is the
coherency scale parameter.

C.3 Von Karman isotropic turbulence model

The
longitudinal velocity component spectrum is given in this case by the
non-dimensional equation:

where

f is the frequency in Hertz;

L = 3,5?1 is the
isotropic integral scale parameter; and

?1 is the longitudinal standard deviation at hub height.

The lateral and vertical
spectra are equal and given in non-dimensional form by:

where

L is the same isotropic scale parameter as used in Equation (C.4); and

?2
= ?3
= ?1,
are the wind speed standard deviation components.

The coherency is given by:

Where

r
is
the separation between the fixed points;

L is the isotropic turbulence integral scale;

? (.) is the gamma function; and

K(.)(.) is the fractional-order, modified Bessel function

.

Equation (C.6) can be approximated by the
exponential model given in Equation (C.3), with Lc replaced by the isotropic scale parameter L.