How convergent- divergent nozzle work?

vvishwaskumar · 2009-07-27T16:44:52+00:00

how convergent- divergent nozzle works in relation to pressure/velocity, while steam is passing through it... i m little confuse

Aashish Joshi

Member • Jul 28, 2009

Convergent-Divergent nozzles are used to increase the flow of gas to supersonic speeds (as in the case of rockets). Their is cross-sectional area first decreases and then increases. The area where the diameter is minimum is called the throat.

As the gas enters the converging section, its velocity increases, considering the mass flow rate to be constant. As the gas passes through the throat, it attains sonic velocity(mach number =1). As the gas passes through the divergent nozzle, the velocity increases to supersonic(mach number >1)

Please refer to the fine article given in wikipedia, <a href="https://en.wikipedia.org/wiki/De_Laval_nozzle#Operation" target="_blank" rel="nofollow noopener noreferrer">De Laval Nozzle Operation</a>, for detailed information and pictures.

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Tkelly

Member • Aug 4, 2009

For the convergent-divergent nozzle the calculation from the inlet to the throat (convergent) is usually an expansion to sonic conditions. From convergent to divergent the flow is expanded supersonically according to the prescribed area ratio A(divergent)/A(convergent). If the nozzle exit static pressure Ps9 comes out higher than ambient pressure then the solution has been found and the calculation is finished.

Tom
<a href="https://www.indovance.com" target="_blank" rel="nofollow noopener noreferrer">CAD Outsourcing Services India | Indovance Inc</a>

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nany_mech

Member • Aug 5, 2009

C-D nozzle is designed for attaining speeds that are greater than speed of sound. the design of this nozzle came from the area-velocity relation

(dA/dV)=-(A/V)(1-M^2)

M is the mach number ( which means ratio of local speed of flow to the local speed of sound) A is area and V is velocity

The following information can be derived from the area-velocity relation

1. For incompressible flow limit, i.e. for M tends to zero, AV = constant. This is the famous volume conservation equation or continuity equation for
incompressible flow.

2. For M < 1, a decrease in area results in increase of velocity and vice vera.
Therefore, the velocity increases in a convergent duct and decreases in a
divergent duct. This result for compressible subsonic flows is the same as that
for incompressible flow.

3. For M > 1, an increase in area results in increase of velocity and vice versa, i.e. the velocity increases in a divergent duct and decreases in a convergent duct.This is directly opposite to the behavior of subsonic flow in divergent and convergent ducts.

4. For M = 1, dA/A = 0, which implies that the location where the Mach number is unity, the area of the passage is either minimum or maximum. We can easily show that the minimum in area is the only physically realistic solution.

One important point is that to attain supersonic speeds we have to maintain favorable pressure ratios across the nozzle.

One example is : to attain just sonic speeds at the throat, pressure ratio to e maintained is (Pthroat / P inlet)=0.528.

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krak000

Member • Jul 14, 2011

friend, i have a doubt...........
in a convergent Nozzle, pressure decreases n Velocity increases. If Velocity Increases, Its Accelaration also increases. So, Force also increases. So, Pressure has to be increased...... But y it is decreasing?

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ShrinkDWorld

Member • Jul 16, 2011

Actually in nozzle the pressure energy is converted in to velocity energy. In my view, this dynamic theory is not suitable for nozzle. Our expert shall explain it in detail.
I think the force required for increasing velocity is provided by pressure. And so it must be decreases. I may be wrong!!

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adilgrt007

Member • Nov 15, 2011

hi i am little confused fluid flowing
at low speeds the velocity of a fluid increases when the area through which it is traveling decreases. I am curious as to why a fluid traveling faster than the speed of sound increases its velocity when its area is increased.

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pelujhonny

Member • Aug 8, 2014

"I am curious as to why a fluid travelling faster than the speed of sound increases its velocity when its area is increased."

All has to do with the mass flow rate which must be constant at all times, that is, the same amount of mass coming in must come out the nozzle. For a nozzle the mas flow rate is equal to density x velocity x cross sectional area of nozzle. That is: dVA = constant.

At low velocities the density is constant and therefore as the area gets smaller (convergent nozzle) the velocity must increase to keep dVA constant. This is the case we are used to in our day to day lives.

At speeds closer to the speed of sound, the density is not a constant any more. At these speeds the fluid is sort of stretched out and less dense: the higher the velocity the lesser dense the fluid becomes. At this point we notice that the density and the velocity work in opposite directions in the quantity dVA, that is, meanwhile more V brings dVA higher, less d brings dVA lower. If in the nozzle we continue to make A smaller (convergent), eventually we will reach the point where d out-powers V in the expression dVA and the velocity cannot go higher anymore. In other words, dV reaches its maximum. Any increase in V will cause a decrease in d such as the quantity dVA would be smaller and this is not possible, dVA must be a constant. The value of V when this maximum happens is the speed of sound for this particular fluid and conditions. To make this point clearer, the speed of sound is not a constant, it varies with the fluid, the temperature, etc.

By the way, since the quantity dV is at its maximum, the mass flow rate dVA is at its maximum as well. In other words, it is impossible to increase the mass flow rate no matter what and the nozzle is said to be choked.

After the speed of sound is reached, if we increase A (divergent nozzle), V will continue to go up and d will continue go down in such a way that dVA will remain still constant. Effectively the fluid now behaves the opposite way, it will increase its velocity as the area increases and all because the inverse relationship between the density and the velocity of the fluid.

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DADISETTY GOVIND

Member • Aug 15, 2014

CAN any solve my crazy doubt.if gas is sent through nozzle its speed increse more than sound,what will happen if sound is sent through nozzles(is it possible).while the gas passes into nozzle sound will be crated or not,if it is created that means it is travelling with the same speed of that gas na.

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BIKRAM NONGMAITHEM

Member • Oct 3, 2015

da/A=(1/isotropic constant of superheated steam i.e 1.3 )(dp/P)(1-m^2)(m^2)
where dp=initial convergent pressure- final end of divergent nozzle pressure=p1-p3=neagtive.similarly for da=-ve.
so the term (1-m2)(m2) is positive.This implies that m<1.i.e m=ratio of speed of sound by speed of steam
speed of steam found to be greater than speed of sound.

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Chanpreet singh

Member • Nov 15, 2015

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Chanpreet singh

Member • Nov 15, 2015

i also have a doubt that why there is a sudden decrease in the area from the inlet to throat while it is increasing gradually at outlet why not suddenly?

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johann Wegmann

Member • Mar 11, 2016

Hi Gentlemen,Area/velocity,EQUATION,in conical divergent nozzle,M>1,adiabatic,I need help to integrate this expression,
dA/A=(M exp 2-1)dV/V,A =indep.variable,
M Mach Nr.V increases with A,ok,Integration lands on Natural Logs,and I give up,I am sorry,please helpme with any size nozzle.Thanks Johann Wegmann

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pranabjyoti

Member • Jul 1, 2016

In my opinion, convergent and convergent-divergent not only convert the pressure but also part of internal energy into motion. That's why in steam turbines, stators are placed between rotors. The rotors convert pressure of steam into motion and thereby using that to rotate itself. While the stators remain static and convert internal heat of steam into pressure. If we look at the cross section of a stator, we can see that the passages are designed in such a way that if they are straighten up, they will simply look like a convergent nozzle.

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rayhan badsha

Member • Mar 8, 2018

show that the maximum discharge of air through a converging diverging nozzle would take place if the velocity at the throat of the nozzle is sonic.show the details.

nany_mech
C-D nozzle is designed for attaining speeds that are greater than speed of sound. the design of this nozzle came from the area-velocity relation

(dA/dV)=-(A/V)(1-M^2)

M is the mach number ( which means ratio of local speed of flow to the local speed of sound) A is area and V is velocity

The following information can be derived from the area-velocity relation

1. For incompressible flow limit, i.e. for M tends to zero, AV = constant. This is the famous volume conservation equation or continuity equation for
incompressible flow.

2. For M < 1, a decrease in area results in increase of velocity and vice vera.
Therefore, the velocity increases in a convergent duct and decreases in a
divergent duct. This result for compressible subsonic flows is the same as that
for incompressible flow.

3. For M > 1, an increase in area results in increase of velocity and vice versa, i.e. the velocity increases in a divergent duct and decreases in a convergent duct.This is directly opposite to the behavior of subsonic flow in divergent and convergent ducts.

4. For M = 1, dA/A = 0, which implies that the location where the Mach number is unity, the area of the passage is either minimum or maximum. We can easily show that the minimum in area is the only physically realistic solution.

One important point is that to attain supersonic speeds we have to maintain favorable pressure ratios across the nozzle.

One example is : to attain just sonic speeds at the throat, pressure ratio to e maintained is (Pthroat / P inlet)=0.528.

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rayhan badsha

Member • Apr 5, 2018

show that the maximum discharge of air through converging diverging nozzle would take place if the velocity at the throat of the nozzle is sonic. show the details.

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MSAMBA CHACHA

Member • Dec 13, 2018

What is afterburner

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