Wastegate Calculation: Formula & Guide

Hey everyone, I've been browsing this forum for a while now and I've noticed there are a lot of great people here. Maybe someone can help me with a small problem I'm having.
I'm trying to calculate the specifications for a wastegate for a turbocharger, but I'm having trouble finding relevant information. Could someone recommend some resources where I can find formulas, literature, tips, and tricks – basically, anything about the design and operation of a turbocharger wastegate? I'm looking for everything from the basics to calculation software, flow simulation, and more. I'd appreciate any advice you can offer.
Sure, here is the translation of the text from German to English:

'cu Frank'

Hello bomber!

You've certainly taken on quite a bit .
I hope you have the necessary basic knowledge (physics, thermodynamics, fluid mechanics), because it will be really tough without it!

You should focus primarily on gas dynamics.
For a rough estimate, if you can provide me with the necessary data, I might be able to find the time. However, I doubt I can burden our CFD (Computational Fluid Dynamics) software with your problem, as it's already booked out for months in advance.

Just post some data and facts (turbocharger characteristic map, mass airflow, etc.), let's see if we can make anything of it.

Regards,
Alex.

Hi donalexo,
It's not really something you can just say, it's about general turbocharger development, and I was just told about the wastegate. The general function and so on are clear, but unfortunately, I'm missing a bit of the basics when it comes to the design, so I'm looking for literature that describes some of it, maybe even something I can use as a starting point.
The fundamentals of thermodynamics, physics, and related subjects are all covered; we definitely went into enough detail about those topics during our studies.
Unfortunately, I don't have any specific details about the engine yet, so I'm currently looking for general information or procedures.
Who knows, maybe there's something there.
Sure, no problem.
Sure, here is the translation of the text from German to English:

'cu Frank'

Hi, I'm a little smarter now.
Roughly speaking, I first need to determine the maximum flow rate coming from the engine, and the maximum flow rate that the turbine can handle, which I can find using the maximum rotational speed. This rotational speed is, in turn, determined by the maximum circumferential speed (which depends on the material). The difference between these flow rates gives me the maximum bypass flow. (Don't forget safety margins and all that). Then, I can calculate the minimum area of the wastegate based on the flow rate, considering factors like the speed of sound and cavitation.
Have I forgotten, overlooked, or completely misunderstood something fundamental?
'Also, I'd also like to know how this works with a twin-scroll turbine, a forced induction system. Is the wastegate connected to both channels? Does anyone know where something like this has been installed before, and how?'
Maybe you have some photos or something, and I would really appreciate any help you can offer.

Sure, here is the translation of the text from German to English:

'cu Frank'

Hello Bomber!

It seems like you're mixing up some technical terms a bit. So, let's go through them one by one:

I assume you're referring to a staged turbocharger when you mention a two-stage turbine. This is then called staged charging. I'm actually only familiar with the term "boost" in the context of naturally aspirated engines, where the intake manifold lengths are adjusted to utilize the air column's inductance to get more air into the cylinders.

You also used the term "cavitation." In the context of fluid flows, cavitation refers to a situation where the local vapor pressure is exceeded, leading to a two-phase flow that contains both liquid and gas. However, in your case, it's a pure gas flow, so cavitation cannot occur.


Now, let's move on to the interpretation:

Generally, the approach of determining the maximum mass flow rate or volumetric flow rate of the engine is correct. Determining the mass flow rate is still relatively simple, but deriving the volumetric flow rate is not so trivial. I think it's better to determine the range of mass/volumetric flow rates from idle to maximum speed, in order to also take into account the response behavior at low speeds and loads.
You should definitely use an h-s diagram for exhaust gases (are there such things?) and have good knowledge of the field of gas dynamics for these considerations.

Unfortunately, I don't have time right now, but perhaps I can provide some further guidance on the interpretation later this evening.

Regards,
Alex.

I assume that when you mention a two-stage turbine, you mean a register turbocharger.

no.

'Two-stage' means that the turbine is fed by two separate 'nozzles.'
'This is typically done in larger, multi-cylinder engines. This ensures that the exhaust flow is distributed appropriately to each cylinder. Otherwise, there would be cross-flows between the cylinders, and nothing would reach the turbine.'
Typical applications are located at the loading dock .
http://www.egarrett.com/technology/tech_twin_scroll.jsp?justlist=1&l1id=2&l2id=2&l3id=1

'Shock charging' and 'congestion charging' indicate the 'charging principle' of the charger.

In a turbocharged system, the exhaust gas flows directly from the exhaust manifold to the turbine, which is therefore driven intermittently. This is the most common, and in fact the only feasible, type of turbocharging for small engines.
However, it has a low efficiency.

In a supercharging system with exhaust gas recirculation, the exhaust gases first enter a 'collection chamber' and are then fed to the turbine at a relatively constant pressure. This only works with large engines that do not experience significant load and speed fluctuations, such as ship diesel engines and generators.

CU Gremlin.

@ Gremlin
Yep, definitely two-stroke.
But isn't it true that, in the case of a two-stage system, I'm more likely to have surge charging? Or would two collection tanks be a possibility for surge charging?

@donalexo
Mmm, you're right, I got the cavitation part mixed up, but am I correct in thinking that when designing the cross-sectional area, I need to make sure the flow doesn't reach the speed of sound?

@all
Does anyone know what a wastegate looks like on a twin-scroll turbocharger? Does it have one or two valves?

cu and best regards.

Frank.

but isn't it true that I'm more likely to have forced induction with a twin-turbo setup?

Regardless, forced induction is (predominantly) used in the automotive sector because the charging pressure and flow rates are too low for other methods. In automotive applications, you can only use forced induction (or approximate it) because the operating conditions of the engine are anything but stationary.
That's why the running gear is kept as small as possible.


@all
Does anyone know what a wastegate looks like on a twin-scroll turbocharger? Does it have one or two valves?


In my opinion, two are needed, one for each collection pipe.

CU Gremlin.

Okay.

While I don't have a formal degree, I'd like to add a few thoughts.

You don't need to worry about cavitation; as donalexo already mentioned, it only occurs in liquids.

To accurately calculate a wastegate, you'll need to start with the turbocharger design. Ultimately, you can't determine how much mass flow needs to bypass the turbine if you don't know how much the turbine itself consumes. Additionally, the effects of the air intake system and the properties of the gases before the turbocharger also play a role.

If you're not too concerned about precise specifications and you already have the actual turbocharger, I would suggest, in your place, simply installing a wastegate that's too large and compensating for that disadvantage through adjustment.

It won't be that simple, for example, to determine the moment of inertia of the turbocharger shaft in an assembled charger.
Für einige grundlegende Formeln empfehle ich dir die Seite 402 aus Handbuch Verbrennungsmotor (2. (Edition)

Philipp

Hi, thanks so much for all the help.
@euwing
Okay, I have the data for the charger (or I could obtain it), as this is largely a theoretical project, involving design and construction (CAD).

'In addition, the effects of the suction line and the gas properties before the compressor also play a role.'
What exactly do you mean by 'swallowing line,' and what specifically should I pay attention to?

And do you perhaps have an ISBN number for the manual, or could you send me the aforementioned page electronically ?

cu and best regards.
Frank.

Throat line: Intake/loading capacity of the loader.

Unfortunately, I don't have a scanner! ISBN: 3-528-13933-1.
But that book cost 74 euros back then; it's better to check a library.
Wenn du fertig bist mit dem CAD, kannst du mir mal die Datei zukommen lassen. Würde mich freuen. I have Solid 2004!
Good luck.

@Donalexo:
'As far as I know, forced induction is typically used with naturally aspirated engines, where the intake manifold runner lengths are tuned to utilize the air column's inductance to help force more charge into the cylinders.'
What you likely mean is the resonance charging or scavenging effect. We talk about register charging when we connect multiple turbochargers in series.

Best regards, B_Man23.

@B_Man23:

You are absolutely right, I confused forced induction with resonance charging .

Regards,
Alex.