How does the BMW M4 GTS achieve low water consumption in its water injection system?

Question

Bosch recently made waves when it announced plans to offer the M4 GTS' water-injection system to other mass-produced vehicles.

Now water injection isn't a new concept; Bruce Crower put the six-stroke engine in the limelight about a decade ago, but articles were quick to point out that it would require a significant supply of clean water:

Preliminary estimates suggest a Crower cycle engine will use roughly as many gallons of water as fuel.

What prompted this question is Bosch's claim that the water tank needs to be replenished once every 1800 miles (roughly 2900 km).

That is an order of magnitude less water consumption. How come?

From the video in the linked article, it doesn't look like they are doing any recycling/filtration of the water.

Of course, it could be that the amount of water required is teensy-weensy, but I don't see how it would explain the order-of-magnitude difference between this Bosch design and the Crower six-stroke.

Answer 1

Aha, here is what I believe is the true answer.

Whereas the MotoGP M4 draws its water from a manually filled tank in the boot, however, BMW's latest water-cooled prototype is fitted with a water recovery system that constantly tops itself up with condensed water from the air conditioning system.

Funny, my brother and I were discussing water injection, and we suggested the idea of using water from the AC system. Thought I'd research it to figure out if anyone had thought of it, and... tada!

Answer 2

There are two major differences in what's going on with either engine.

The Crower engine design utilizes six-strokes to accomplish what it's doing. It uses the extra two strokes to create an extra power stroke (so you'll have two power strokes per three revolutions of the crankshaft instead of the Otto cycle's single power stroke for every two turns). The idea is to utilize the heat energy which is already there, which would otherwise be going out the tail pipe or getting syphoned off through the radiator. Water is being used all the time to accomplish this.

What BMW is using water for is more the typical idea of water injection. That being it is using it to control detonation in the cylinder. Unless the engine needs it under stressful situations, the water isn't going to be used. Then when it is used, it's only used sparingly ... just enough to ensure detonation is squelched. This allows for higher power outputs from the engine without fear of killing the engine.

For a little background on why using water is so good in either situation, there are several reason:

1. Expansion rate of water as it turns to steam. At 300°C water will expand at a rate of about 3300:1. My understanding is this is far in excess of the expansion of air/fuel as it's burned. Also, if you go hotter with steam, it will expand more.
2. Water as it turns to steam tends to clean the combustion chamber and cylinder. A clean engine is a happy engine.
3. Water acts as a detonation reducer. This applies more towards the BMW way of doing things, but is still applicable. Water can in effect add around 10 points of octane to fuel (using the R+M/2 method). Instead of 91 octane fuel, you now have 101 octane fuel ... good stuff.
4. Water in the induction system creates a more dense intake charge due to the absorption of energy. Water can suck up a lot of it. This again, applies more towards the BMW way of doing things.
5. Since water injection reduces combustion temperatures, it greatly reduces the amount of Nitrogen Oxides (NOx) which is created when things get too hot. Of the three major pollutants which are commonly created in the combustion process (Hydro-carbons [HC] and Carbon Monoxide [CO] being the other two), NOx formations are probably the most harmful to air breathers like you or me.

There are probably more reasons, but these are a few of the good ones.

Answer 3

From http://www.m-power.com/_open/s/varlink2.jsp?id=3301&lang=en:

Located in the boot of the BMW M4 MotoGP Safety Car is a water tank with a gross volume of about five litres, which houses the water pump, sensors and valves. The pump and complete system of sensors and actuating elements are controlled by the engine electronics, which have been upgraded accordingly. In practice, the pump feeds the water to the injectors at a pressure of ten bar, whereby the appropriate volume is supplied depending on load, engine speed and temperature. This ensures that water consumption is kept to an absolute minimum. In rigorous action out on the racetrack, it is always necessary to refill the water supply whenever the car must refuel. During standard operation, the intervals between water refills are considerably longer, depending on the driving style. Even when driving faster on the motorway, it is only necessary to refill the water container roughly every five stops for refuelling. To ensure the system is as suitable as possible for daily use, it does not require any additional maintenance.

In other words, for normal usage on your car, the amount of water required to prevent engine knocking is so minimal that a 5 litre tank is sufficient to do a significant amount of mileage.

Great question, BTW.

Answer 4

My Musings

The stark difference between the two approaches becomes self-evident; they really are orders of magnitude apart:

• Water injection requires an average of 9 cc/min
• Crower six-stroke requires an average of 572 cc/min

Calculations, assumptions listed below.

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The Bosch setup

This article claims that the water injection system provides an additional 80 °F (44 °C) of cooling:

Depending on the design and size of the system, and the aerodynamics of the vehicle, it is only possible to use an intercooler to reduce the intake air temperature by as much as 160° F before it enters the plenum chamber. This means that simply rising engine power by increasing boost pressure is not an option as it would mean exceeding the knock threshold.

This is where the BMW M division’s solution comes in: if water is injected in a fine spray mist into the intake plenum chamber, it is possible to reduce the temperature of the intake air by an additional 80° F.

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Great. Let's crunch some numbers:

• Let's assume the M4 engine averages 1500 RPM during regular operation.

  The rate of air volume ingested by the engine at this speed is:

  = 2979 cc * 1500 RPM / 2    # divide by 2 because four-stroke
  = 2,234,250 cc / min
  = 37 liters / second
  = 0.037 m3/s
  

• The twin turbos develop 18.1 psi at peak boost, so let's guesstimate 4-5 psi boost on average.

  Absolute pressure at intake valve = 14.7 + 4 = 18.7 psi
  

  Assuming a decent intake air temperature

  Air density at 18.7 psi, 50 °C = 1.39 kg/m3
  

  (Fortunately for us, this is a direct injection setup, so WolframAlpha's thermodynamic properties for air are useful)

• Putting two and two together, the average mass air flow rate (@ 100% volumetric efficiency) is:

  Mass air flow rate = 1.39 kg/m3 * 0.037 m3/s
                     = 0.0514 kg/s
  

  (This does beg the question: what is a reasonable volumetric efficiency to assume here? More on that later)

• How much energy does it make air change temperature under these conditions?

  Apparently 719.5 J/(kg-K).

• And how much energy does it take to convert water to steam?

  Latent heat of vaporization of water = 2,230,000 J/kg

  That is an epic amount of energy. It dwarves the specific heat of water, which is 4200 J/(kg-°C).

• So, what's the average water flow rate required?

  @ 100% VE, the energy per second required to change air temperature by 44 ˚C is:

  = m • Cv • ( T1 - T2 )
  = 0.0514 • 719.5 • 44
  = 1630 J
  

  That doesn't translate to much water:

  Require water mass flow per second:

  = Energy ÷ ( latent heat of vaporization )
  = 1630 J / 2,230,000 J/kg
  = 0.00073 kg
  = 0.73 g
  

  In other words, roughly 44 cc / minute @ 100% VE.

  If the real-world VE is 20%, which is to be expected at part-throttle, that figure plummets to around 9 cc / minute.

• Per anonymous2's answer the water tank is 5000 cc

  So at 9 cc / min, the water tank should last around 9.25 hours.

  If the average vehicle speed at 1500 RPM is something like 45 mph, the tank should last around 40 hours.

  The 4x discrepancy could be down to one of the many assumptions made. At least the calculated value is in the right ballpark.

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The Crower six-stroke

(This one's pretty straightforward)

• The minimum amount of water required to enact a reasonable secondary power stroke...

  would be one in which steam occupies the displacement of the cylinder:

  Steam required = displacement * RPM / 3  # once per three crank revs
                 = 2979 cc * 1500 RPM / 3
                 = 1,489,500 cc / min
  

  That's roughly 1500 l / min, or 0.25 m3 / s

• How much water is required for that?

  Depends on the cylinder head temperatures, but assuming 0.8 bar and 350 °F, the expansion ratio is roughly 2600:1.

  So total water flow rate required:

  = 1,489,500 cc / min ÷ 2600
  = 572 cc / min