Converging Diverging Restrictor

[ritwikdas18]

I am from BITS Pilani , India. Our team uses a turbo. So according to the rules changes this year, the restrictor should be ahead
of the throttle body exposed to atmospheric pressure. According to my calculations for a maximum mass flow rate and minimum
pressure loss for a converging nozzle,when outer area of converging nozzle tends to 20mm ie convergent area ,368

http://www.wolframalpha.com/input/?i=maximize+%28x%5E%2810%2F7%29%29*%281-x%5E%282%2F7%29%29%2F%281-0.75*x%5E%2810%2F7%29%29+over+%5B0%2C1%5D

Refer to the attachment before reading this.
Since p1 is always ambient pressure and A2 is 20mm we have to maximize mass flow rate keeping p1/p2 to a maximum.since p1/p2 lies between 0 and 1 our maxima also lies between that. So I used wolfram Alpha for various A2/A1 ratios and found that as A1 tends to A2. mass flow rate increases as well as pressure loss decreases. And Since compressor inducer diameter is only 22.63 mm, it is not much of a diverging thing to do.


Can someone logically guide us whether a converging diverging nozzle is necessary or whether my calculations are correct

[apalrd]

You would like the peak mass flow of air through the restrictor, correct? The area of the restrictor is easily calculated from the diameter (20mm or 19mm)


For any given nozzle and fixed temperature, the flow across the nozzle is determined by the pressure ratio across the nozzle (this is why the upstream pressure must be atmospheric and not boost).

The simple answer:

As you decrease the pressure ratio to a number less than one (so there is a pressure differential across the nozzle), air will flow through it, with some velocity. When the velocity of the air reaches mach 1, then the restrictor is 'choked', as the air will not happily travel faster.

For air the critical pressure ratio is known to be 0.528, which corresponds to a flow velocity of mach 1.

So to find the choked flow, you must solve for the flow given an upstream density of atmospheric (whatever your baro pressure and ambient temperature is, or assume STP) and a velocity of mach 1. This will tell you the mass flow. You know that the downstream pressure will be 0.528 * baro, so you then have the mass flow and pressure entering the compressor for a forced induction setup.

This doesn't mean that a pressure ratio of 0.528 is most efficient, due to pumping work, but it is where you will maximize the restrictor flow.

Through the googles, I found a NASA overview of nozzle flows (it's kinda focused on rocket engines, but the concepts carry over quite well). http://www.grc.nasa.gov/WWW/k-12/airplane/mflchk.html

[ritwikdas18]

The number 0.528 is when A2/A1 is zero. But that is not correct in our case since A2=20mm .The number tends to 1 as A1 approaches A2.Moreover Velocity of Mach 1 is not achieved at the inlet but rather at the throat for maximum mass flow rate

[apalrd]

The number 0.528 is when A2/A1 is zero. But that is not correct in our case since A2=20mm .The number tends to 1 as A1 approaches A2.Moreover Velocity of Mach 1 is not achieved at the inlet but rather at the throat for maximum mass flow rate

Yes, this is true, the velocity is at the throat.

But that's all we need to find the mass flow rate and downstream pressure.

[ritwikdas18]

I know how to calculate downstream pressure and maximum mass flow rate. My Question is "Do we need a Converging restrictor(nozzle) for the turbocharged car?" and why yes or why
no. Because my calculations say we don't need it, but the trend is otherwise. And if your answer is Yes then what should be A1(Inlet area of Converging Restrictor)?

[apalrd]

I know how to calculate downstream pressure and maximum mass flow rate. My Question is "Do we need a Converging restrictor(nozzle) for the turbocharged car?" and why yes or why
no. Because my calculations say we don't need it, but the trend is otherwise. And if your answer is Yes then what should be A1(Inlet area of Converging Restrictor)?


In general, anything abrupt in the air path is bad.

So, generally, a cone is used on the inlet of the restrictor. However, the inlet A1 is not really defined, it's just 'big'.

In general, it is the same size as the outlet of whatever air filter is used.

[ritwikdas18]

Air filter will be selected based on A1 not the other way round. Can you justify your claims with calculations? If I say to the design judges ,"In general we used a big A1" then we will score zero.

[apalrd]

Air filter will be selected based on A1 not the other way round. Can you justify your claims with calculations? If I say to the design judges ,"In general we used a big A1" then we will score zero.

Since its a tradeoff, I have always based that measurement to give a reasonable ratio (e.g. 2x the throttle bore for non-turbo) since anything bigger won't package on the car.

[ritwikdas18]

I think I am back to square 1 ."Should we or should we not go for a converging diverging restrictor for a turbo setup according to new 2015 rules? " Why Yes or why NO?

[Mbirt]

Of course a converging-diverging nozzle design is not required. Feel free to use a plate orifice.

[Jay Lawrence]

Ritwik,

You cannot ask "do we need design X or design Y for this year?" The answer could be: don't run a turbo.
If you know how to calculate mass flows through a nozzle then you know what you need to do! You will have some inlet diameter D1 based on your air filter size, you have an outlet diameter D2 (in your case 22.63mm) and you have a minimum throat diameter (20mm, or 19mm if you are running E85). The length of the restrictor (and, if not known, D1) is then determined by packaging constraints and CFD analysis.