Brake heat rejection concept

[olefud]

Calculating a Re is somewhat arbitrary given the large variation in the velocity and temperature of the rotor, Re being directly proportional to the speed and inversely so to the air viscosity, which increases with temperature. Air temperature immediately adjacent the rotor is not measured in conventional dyno testing.

Just from observation, the boundary layer appears to be laminar away from the pad when the rotor is glowing dark red based on the incandescing particles. On the other hand, some of these heavier ?such particles escape immediately following the pad. My working assumption is that a heat stressed rotor has a laminar boundary layer though it may take a while to form after the pad disruption.

Re is arbitrary by definition but it is an important indicator, especially when trying to figure out whether a particular flow structure is laminar or turbulent.

My back of the envelope calcs suggest a Re of the order of 250,000 - 400,000 at ambient air temperatures and 50,000 - 80,000 at temperatures of 400 degC, halving again to 30,000 - 40,000 around 800 deg C depending on what assumptions you make about rotor/air speed and dimensional scales. These numbers do show the dramatic effect of the change in density and dynamic viscosity over temperature that you have often mentioned. However they are all well north of the (yes arbitrary) threshhold between laminar and turbulent flow around Re = 5000, to get to this number vehicle speed would have to be reduced by a factor of 6.

I guess I would like to challenge the assumption that the flow patterns you are observing are laminar. I suggest that what you are observing are sections of relatively stable flow structure, due to favourable pressure gradients and relatively small length scales due to the flow being adjacent to the rotor, but it is still very turbulent.

I realise this doesnt actually shed much light on your situation but to me its an important distinction.

Your point is taken and parallels my original thinking. However, testing has developed a few anomalies and empirical results that raise new questions.

With reasonable assumptions, braking at 120 MPH allows about .03 seconds between a rotor point passing the pad and arriving again. Testing has shown that vanes closely trailing the pads are of diminished effectiveness while those leading the pads are quite effective. Assuming –as I do- that the pads effectively disrupt the rotor boundary layer, there are rapid changes in conditions, particularly temperature, during these few tenths of a second. The boundary layer forms, or is forming, and apparently carries along cooler air that acts on the pads. Given, if you will, these dynamic, rapidly changing conditions, and the probable nascent early boundary layer, Re offers a bit too much certainty more appropriate for established, steady-state situations.

Since, in my view, the concept deals with a new mechanism, I’m working to conservatively sort what is known while being open to theories and explanations.

[riff_raff]

Of course, a laminar flow boundary air layer is also an effective form of thermal insulation.

I disagree, air is only an effective form of insulation when it isnt moving. Yes convective heat transfer coefficients are lower for laminar flow, but they are not zero.

This is why the air-film cooling of turbine engine exhaust nozzles is so effective.

Doesnt this contradict your previous sentence?

To the contrary, boundary airflows are efficient insulators when they are laminar, and not just when they are static. This would imply that they can have movement, as long as the boundary airflow remains attached to the adjacent surface. This the primary reason why film cooling of turbine blades is so effective. There is a great effort made when deciding where to locate the holes used for film cooling of turbine blades/nozzles. The holes are located such that the cooling airflows remain attached to the blade surface. It's only when the boundary layer becomes turbulent or separates that the heat transfer rate to the core airflow increases.

[olefud]

Of course, a laminar flow boundary air layer is also an effective form of thermal insulation.

I disagree, air is only an effective form of insulation when it isnt moving. Yes convective heat transfer coefficients are lower for laminar flow, but they are not zero.

This is why the air-film cooling of turbine engine exhaust nozzles is so effective.

Doesnt this contradict your previous sentence?

To the contrary, boundary airflows are efficient insulators when they are laminar, and not just when they are static. This would imply that they can have movement, as long as the boundary airflow remains attached to the adjacent surface. This the primary reason why film cooling of turbine blades is so effective. There is a great effort made when deciding where to locate the holes used for film cooling of turbine blades/nozzles. The holes are located such that the cooling airflows remain attached to the blade surface. It's only when the boundary layer becomes turbulent or separates that the heat transfer rate to the core airflow increases.

A turbulent boundary would likely have enhanced intralayer heat transfer. However, as long as it was a coherent layer, heat transfer from the boundary layer to the flow would seemingly be minimal.

[riff_raff]

A turbulent boundary would likely have enhanced intralayer heat transfer. However, as long as it was a coherent layer, heat transfer from the boundary layer to the flow would seemingly be minimal.

That's exactly my point. The heat transfer process from the metal rotor surface to the boundary airflow is more efficient than the heat transfer process from the boundary airflow to the core airflow. Then there is also the greater relative deltaT between the rotor surface and boundary flow than that between the boundary flow and core flow to consider. By making the flow at the rotor surface turbulent, you create a situation where the temperature of the airflow over the rotor surface is much lower.

[olefud]

A turbulent boundary would likely have enhanced intralayer heat transfer. However, as long as it was a coherent layer, heat transfer from the boundary layer to the flow would seemingly be minimal.

That's exactly my point. The heat transfer process from the metal rotor surface to the boundary airflow is more efficient than the heat transfer process from the boundary airflow to the core airflow. Then there is also the greater relative deltaT between the rotor surface and boundary flow than that between the boundary flow and core flow to consider. By making the flow at the rotor surface turbulent, you create a situation where the temperature of the airflow over the rotor surface is much lower.

The mechanism of the rotor boundary layer is, for me, a bit too involved to solve with static modeling. In addition to the short duration, dynamically changing nature of this layer, there’s also the matter of rotary motion. The temperature profile within the boundary layer suggests that the air will segregate according to density which varies significantly according to temperature, i.e. the cyclone separator effect. On the other hand, the boundary layer is in essence a slice of a vortex. Thus Coriolis forces will tend to maintain flow to a common radius auguring against turbulent flow in the boundary layer as in a proper vortex. While the vanes can be spaced well beyond rotor runout, Coanda effect prevents this positioning as indicating the boundary layer thickness.

Given that a relatively fat boundary layer forms in the short period between a rotor point passing the pad and again encountering the pad, heat energy transport intra boundary layer more effective than simple conduction seems probable. However, since the rotor temperature is significantly reduced by the vanes, it would seem that such heat transport is confined to the boundary layer which is rather impervious to external forced convection cooling. That this effect doesn’t become pronounced, or beyond barely noticeable, until higher temperatures are attained strongly suggests that the change in the properties o fair at elevated temperatures drives the phenomenon.

The boundary layer is insulating yet accumulates a good bit of thermal energy in a very short period of time. That I can state with reasonable certainty. Yet it appears to cool the pads; a result opposite of my initial expectations. I still have more to learn.