Makaveli_se7en
Member
Having had to endured a 12 hour flight last week I thought I would use the time to put together a few of thoughts on a subject that I feel is surrounded by internet fallacy and hearsay. So here are my thoughts on turbocharger transient response or "turbo lag". I hope that its not too heavy going and that at least a few of you find it interesting and informative.
Technical Notes on Turbocharger Transient Response
Disclaimer:
Like all good engineers I am starting with my disclaimer: The information below is correct to the best of my knowledge and although I have tried to reason and explain the physics behind the statements some of the comments are based on my own experience and opinion. I also apologise if this is at all patronising or over simplified but I’ve tried to make it as readable as possible for a large range of people.
Introduction:
The following include some of my thoughts on turbocharger transient response. I have written it in a generic style so it is applicable to turbos of all sizes but becomes especially important when looking at high power outputs from small capacity engines e.g. 500bhp+ Pulsars. As such there is no discussion on the relative merits of individual turbo/manifold configurations but instead the information below should allow the reader to make a more informed choice when picking a turbocharger.
The contents of this post will focus solely on the turbocharger in isolation, there are people on this forum that are better qualified to speak on the effects of the multitude of engine parameters that will have an effect on the way the engine responds e.g. CR, cam timing, fuelling, timing etc.
I will expect that the reader has some basic knowledge of how a turbocharger works and what a compressor map looks like. If you don’t then I would suggest the following pre-reading might be useful:
http://www.turbobygarrett.com/turbobygarrett/tech_center/tech_center.html
OK, so what everyone wants to know is “how much turbo lag will setup X have?” To understand this first we need to understand what is lag and what causes lag. For this discussion I will define lag as the time taken between pressing the throttle at low rpm and the turbo producing the desire level of boost to the engine. There are two main factors which will affect this:
• First (and more complex) is what I will refer to as “steady state” effects or "aerodynamic work balance", this can be thought of as how much boost will the compressor supply for a given engine rpm.
• Secondly is what I will refer to as “mechanical transient performance” this is basically how much inertia do the rotating components of the turbo have and what is the resistance to them rotating.
Steady State Performance:
It may seem odd to be talking about “steady state” when discussing transient response but the main factor in governing when the desired boost pressure is obtained is the work balance between the turbine and the compressor for a given rpm. I have called this “steady state” as it work balance would be the same if the engine was held at a constant rpm as well as during acceleration (if someone can think of a better name please feel free to suggest one). If we consider the compressor first the flow (x-axis on the compressor map) is controlled by the engine size, volumetric efficiency and speed, therefore for a given engine we can assume that the flow demand is directly related to engine rpm. The amount of pressure raise that can be created by the compressor for a given flow is dependent on the predominately dictated by the work available from the turbine and compressor efficiency.
m(dot): Mass flow rate
Cp: Specific heat capacity at constant pressure (of air)
Eta: Compressor efficiency
T1: Inlet temperature
P1: Inlet Pressure
P2: Boost Pressure
Gamma: Specific heat ratio (of air)
The equation above shows how to calculate the work required for a given point on the compressor map. As stated above m(dot) is controlled by the engine (and fixed for a given rpm), Cp, gamma, T1, P1 are all assumed to be constant for this analysis (although it can be seen that minimising inlet temperature and pressure drop across the air filter will also help). So what we are really interested is P2, which is our boost pressure. It can therefore been seen for a given rpm the key to obtaining the most boost for a given engine point is getting the most work from the turbine and having the most efficient compressor possible. So when looking at compressor maps don’t forget to look at the efficiency islands.
Note: The work in this equation does not include bearing losses which are covered later.
So having looked at the compressor end we’ve seen that one of the key factors in providing boost as soon as possible is getting work from the turbine. Turbines are generally more complex and not as well understood as compressors (imo). In this section I will try to focus on the effects of the housing as this is easier to change and it is very difficult to get decent information regarding turbine wheels.
TW: Work per unit mass
Eta: Turbine stage efficiency
Cp: Specific heat capacity at constant pressure (of exhaust gas)
T3: Turbine Inlet Temperature
P3: Inlet Pressure
P4: Outlet Pressure
Gamma: Specific heat ratio (of exhaust gas)
There are two equations to define the work done produced by the turbine stage. The first (given above) shows the work done over the turbine stage (housing inlet to housing outlet). The equation is for ‘specific work’; so is the work done per unit mass. The mass going through the turbine will be equal to the mass going through the impeller (which we’ve already stated is controlled by engine revs) and the amount of fuel added during combustion. Looking at the equation we can see that the see that as with the compressor the key parameters are the inlet temperature, efficiency and ER (expansion ratio: ratio of outlet pressure over inlet pressure, sometimes called turbine pressure ratio).
To reduce lag we need to maximise the work output from the turbine so the first thing we can do is maximise the inlet temperature, this is possible by minimising the heat lost from the manifold through either thermal wrapping or ceramic coatings.
Next is the stage efficiency, this is a whole area of research in its own right but I will try to summarise the key levers to maximise efficiency here. Firstly if we look at the turbine wheel full back shroud (i.e. no gap between the blades) are more efficient than normal un-shrouded turbine wheels. Another means of maximising the efficiency is reducing the heat loss from the turbine, so again turbo blankets and ceramic coatings will all help with this. Next are frictional losses, this is caused by the boundary layer formed by the gas on the internal surfaces of the housing and the wheel. These losses are highly dependent on the surface finish of the components, so internal ceramic coatings on the turbine housing can reduce these. Another example is the casting process used to make the housing, Borg Warner’s EFR turbine housings are made using an investment casting process and therefore inherently have a better surface finish than the normal sand cast housings. I’ve not seen it done but I want to try polishing the internal surfaces of the housing and the turbine wheel at some point. Generally efficiency information regarding efficiency is given on the turbine swallowing curves and should not to be over looked when selecting your turbocharger.
The third factor; ER also needs to be minimised to provide the most work possible. ER is quite complex to understand for a given mass flow rate (engine speed). The inlet pressure (P3) is partially dependant on the size of the turbine stage as the turbo will act as a restriction to the flow, in this sense it is possible to think of the turbo as an orifice. The size of the orifice is a function of the size of the turbine wheel throat area and the critical area of the housing. The throat area is the smallest the flow passes through area between the blades and is controlled by the blade shape, size of the wheel and the wheel trim. The smaller orifice for flow to pass through the higher the back pressure (P3) generated, this is also part of the reason small turbos will come on boost before larger ones. However the risk here is that the smaller turbine stage will choke (i.e. not be able to provide any more power) before reaching the desired maximum boost pressure/engine speed. The other factor that will determine P3 is the exhaust manifold design, restrictive manifolds such as log manifolds will pressurise more quickly than free flowing tubular manifolds so can be better for lag. Again the risk here is that the more restrictive manifold will result more back pressure on the engine which increase pumping work across the cylinders and reduces the peak power and torque. The outlet pressure (P4) is much easier to understand, simply to increase the turbine work this should be minimised. The best way of doing this is reducing back pressure on the turbo with a free flowing elbow and exhaust system.
Delta_h_rotor : Static Enthalpy change in the turbine wheel
u2: Tip speed at turbine wheel inducer
C(theta)2: Whirl angle at turbine wheel inducer
U3: Tip speed at turbine wheel exducer
C(theta)3: Whirl angle at turbine wheel exducer
The next equation related to the work done by the turbine is known as the Euler (pronounced oiler) equation, named after the guy that came up with it, is given above. This statement says that the change in enthalpy of the gas is a function of the change in tip speed and the change in tip speed and the change in whirl angle. I won’t try to explain enthalpy (definitions can be found on Wikipedia etc.) but it can be thought of as how much work is done by the wheel.
The important part of this is C_theta_2, from the equation it can be seen that by maximising the whirl velocity at the turbine wheel inducer then the work done by the turbine wheel is increased. So what is whirl velocity and how can we increase it? So looking at the diagram below it can be seen that the whirl velocity is the velocity component of the exhaust gas tangential to the turbine wheel. The law of conservation of momentum states that C_theta1 x R1 = C_theta2 x R2. So for a given mass flow a smaller inlet area will result in a higher value of C_theta1 and hence a higher C_theta2; this why smaller housings with the same turbine wheel will produce boost sooner. However as with choosing a small turbine stage an excessively small housing will choke before generating the desired boost level and will require flow to be wastegated to avoid excessive back pressure on the engine.
Having considered the turbine and the compressor as separate entities it is also important to understand the interaction between them. To do this we need to consider a factor called Turbine isentropic velocity ratio (or U/C), this is the ratio of the tip speed (rpm x Pi x Turbine wheel radius) and C is the “spouting velocity”. The spouting velocity is the velocity that the gas would achieve following an isentropic (i.e. no work extraction or losses) expansion from inlet total conditions to the exit static pressure and defined by the equation below.
Cp: Specific heat capacity at constant pressure (of exhaust gas)
To2: Total inlet pressure (Note: definitions of static, dynamic and total conditions can be found here: http://en.wikipedia.org/wiki/Static_pressure)
PR_t: Turbine Pressure ratio
Gamma: Specific heat ratio (of exhaust gas)
Without going into excessive detail we can see from the chart below that the peak efficiency for the turbine occurs at U/C = 0.7. This is true for all radial turbine wheels at all speeds and is a function of the incidence angle between the turbine blades and the exhaust gas. In practice to achieve this; the turbine wheel diameter and impeller diameter should be a closely matched as possible. If an impeller with too larger diameter is used (as is the case with many hybrid turbos) the turbine will operate on the left side of the curve and will not achieve peak efficiency. With modern impeller design which tend to feature more backswept blades it possible to achieve optimal U/C with a slightly larger impeller however I would not recommend going below a turbine wheel to impeller diameter ratio of 0.8.
Note: The reason in most turbochargers the compressor is larger is due to mechanical compromising restricting the diameter of the turbine wheel.
Technical Notes on Turbocharger Transient Response
Disclaimer:
Like all good engineers I am starting with my disclaimer: The information below is correct to the best of my knowledge and although I have tried to reason and explain the physics behind the statements some of the comments are based on my own experience and opinion. I also apologise if this is at all patronising or over simplified but I’ve tried to make it as readable as possible for a large range of people.
Introduction:
The following include some of my thoughts on turbocharger transient response. I have written it in a generic style so it is applicable to turbos of all sizes but becomes especially important when looking at high power outputs from small capacity engines e.g. 500bhp+ Pulsars. As such there is no discussion on the relative merits of individual turbo/manifold configurations but instead the information below should allow the reader to make a more informed choice when picking a turbocharger.
The contents of this post will focus solely on the turbocharger in isolation, there are people on this forum that are better qualified to speak on the effects of the multitude of engine parameters that will have an effect on the way the engine responds e.g. CR, cam timing, fuelling, timing etc.
I will expect that the reader has some basic knowledge of how a turbocharger works and what a compressor map looks like. If you don’t then I would suggest the following pre-reading might be useful:
http://www.turbobygarrett.com/turbobygarrett/tech_center/tech_center.html
OK, so what everyone wants to know is “how much turbo lag will setup X have?” To understand this first we need to understand what is lag and what causes lag. For this discussion I will define lag as the time taken between pressing the throttle at low rpm and the turbo producing the desire level of boost to the engine. There are two main factors which will affect this:
• First (and more complex) is what I will refer to as “steady state” effects or "aerodynamic work balance", this can be thought of as how much boost will the compressor supply for a given engine rpm.
• Secondly is what I will refer to as “mechanical transient performance” this is basically how much inertia do the rotating components of the turbo have and what is the resistance to them rotating.
Steady State Performance:
It may seem odd to be talking about “steady state” when discussing transient response but the main factor in governing when the desired boost pressure is obtained is the work balance between the turbine and the compressor for a given rpm. I have called this “steady state” as it work balance would be the same if the engine was held at a constant rpm as well as during acceleration (if someone can think of a better name please feel free to suggest one). If we consider the compressor first the flow (x-axis on the compressor map) is controlled by the engine size, volumetric efficiency and speed, therefore for a given engine we can assume that the flow demand is directly related to engine rpm. The amount of pressure raise that can be created by the compressor for a given flow is dependent on the predominately dictated by the work available from the turbine and compressor efficiency.
m(dot): Mass flow rate
Cp: Specific heat capacity at constant pressure (of air)
Eta: Compressor efficiency
T1: Inlet temperature
P1: Inlet Pressure
P2: Boost Pressure
Gamma: Specific heat ratio (of air)
The equation above shows how to calculate the work required for a given point on the compressor map. As stated above m(dot) is controlled by the engine (and fixed for a given rpm), Cp, gamma, T1, P1 are all assumed to be constant for this analysis (although it can be seen that minimising inlet temperature and pressure drop across the air filter will also help). So what we are really interested is P2, which is our boost pressure. It can therefore been seen for a given rpm the key to obtaining the most boost for a given engine point is getting the most work from the turbine and having the most efficient compressor possible. So when looking at compressor maps don’t forget to look at the efficiency islands.
Note: The work in this equation does not include bearing losses which are covered later.
So having looked at the compressor end we’ve seen that one of the key factors in providing boost as soon as possible is getting work from the turbine. Turbines are generally more complex and not as well understood as compressors (imo). In this section I will try to focus on the effects of the housing as this is easier to change and it is very difficult to get decent information regarding turbine wheels.
TW: Work per unit mass
Eta: Turbine stage efficiency
Cp: Specific heat capacity at constant pressure (of exhaust gas)
T3: Turbine Inlet Temperature
P3: Inlet Pressure
P4: Outlet Pressure
Gamma: Specific heat ratio (of exhaust gas)
There are two equations to define the work done produced by the turbine stage. The first (given above) shows the work done over the turbine stage (housing inlet to housing outlet). The equation is for ‘specific work’; so is the work done per unit mass. The mass going through the turbine will be equal to the mass going through the impeller (which we’ve already stated is controlled by engine revs) and the amount of fuel added during combustion. Looking at the equation we can see that the see that as with the compressor the key parameters are the inlet temperature, efficiency and ER (expansion ratio: ratio of outlet pressure over inlet pressure, sometimes called turbine pressure ratio).
To reduce lag we need to maximise the work output from the turbine so the first thing we can do is maximise the inlet temperature, this is possible by minimising the heat lost from the manifold through either thermal wrapping or ceramic coatings.
Next is the stage efficiency, this is a whole area of research in its own right but I will try to summarise the key levers to maximise efficiency here. Firstly if we look at the turbine wheel full back shroud (i.e. no gap between the blades) are more efficient than normal un-shrouded turbine wheels. Another means of maximising the efficiency is reducing the heat loss from the turbine, so again turbo blankets and ceramic coatings will all help with this. Next are frictional losses, this is caused by the boundary layer formed by the gas on the internal surfaces of the housing and the wheel. These losses are highly dependent on the surface finish of the components, so internal ceramic coatings on the turbine housing can reduce these. Another example is the casting process used to make the housing, Borg Warner’s EFR turbine housings are made using an investment casting process and therefore inherently have a better surface finish than the normal sand cast housings. I’ve not seen it done but I want to try polishing the internal surfaces of the housing and the turbine wheel at some point. Generally efficiency information regarding efficiency is given on the turbine swallowing curves and should not to be over looked when selecting your turbocharger.
The third factor; ER also needs to be minimised to provide the most work possible. ER is quite complex to understand for a given mass flow rate (engine speed). The inlet pressure (P3) is partially dependant on the size of the turbine stage as the turbo will act as a restriction to the flow, in this sense it is possible to think of the turbo as an orifice. The size of the orifice is a function of the size of the turbine wheel throat area and the critical area of the housing. The throat area is the smallest the flow passes through area between the blades and is controlled by the blade shape, size of the wheel and the wheel trim. The smaller orifice for flow to pass through the higher the back pressure (P3) generated, this is also part of the reason small turbos will come on boost before larger ones. However the risk here is that the smaller turbine stage will choke (i.e. not be able to provide any more power) before reaching the desired maximum boost pressure/engine speed. The other factor that will determine P3 is the exhaust manifold design, restrictive manifolds such as log manifolds will pressurise more quickly than free flowing tubular manifolds so can be better for lag. Again the risk here is that the more restrictive manifold will result more back pressure on the engine which increase pumping work across the cylinders and reduces the peak power and torque. The outlet pressure (P4) is much easier to understand, simply to increase the turbine work this should be minimised. The best way of doing this is reducing back pressure on the turbo with a free flowing elbow and exhaust system.
Delta_h_rotor : Static Enthalpy change in the turbine wheel
u2: Tip speed at turbine wheel inducer
C(theta)2: Whirl angle at turbine wheel inducer
U3: Tip speed at turbine wheel exducer
C(theta)3: Whirl angle at turbine wheel exducer
The next equation related to the work done by the turbine is known as the Euler (pronounced oiler) equation, named after the guy that came up with it, is given above. This statement says that the change in enthalpy of the gas is a function of the change in tip speed and the change in tip speed and the change in whirl angle. I won’t try to explain enthalpy (definitions can be found on Wikipedia etc.) but it can be thought of as how much work is done by the wheel.
The important part of this is C_theta_2, from the equation it can be seen that by maximising the whirl velocity at the turbine wheel inducer then the work done by the turbine wheel is increased. So what is whirl velocity and how can we increase it? So looking at the diagram below it can be seen that the whirl velocity is the velocity component of the exhaust gas tangential to the turbine wheel. The law of conservation of momentum states that C_theta1 x R1 = C_theta2 x R2. So for a given mass flow a smaller inlet area will result in a higher value of C_theta1 and hence a higher C_theta2; this why smaller housings with the same turbine wheel will produce boost sooner. However as with choosing a small turbine stage an excessively small housing will choke before generating the desired boost level and will require flow to be wastegated to avoid excessive back pressure on the engine.
Having considered the turbine and the compressor as separate entities it is also important to understand the interaction between them. To do this we need to consider a factor called Turbine isentropic velocity ratio (or U/C), this is the ratio of the tip speed (rpm x Pi x Turbine wheel radius) and C is the “spouting velocity”. The spouting velocity is the velocity that the gas would achieve following an isentropic (i.e. no work extraction or losses) expansion from inlet total conditions to the exit static pressure and defined by the equation below.
Cp: Specific heat capacity at constant pressure (of exhaust gas)
To2: Total inlet pressure (Note: definitions of static, dynamic and total conditions can be found here: http://en.wikipedia.org/wiki/Static_pressure)
PR_t: Turbine Pressure ratio
Gamma: Specific heat ratio (of exhaust gas)
Without going into excessive detail we can see from the chart below that the peak efficiency for the turbine occurs at U/C = 0.7. This is true for all radial turbine wheels at all speeds and is a function of the incidence angle between the turbine blades and the exhaust gas. In practice to achieve this; the turbine wheel diameter and impeller diameter should be a closely matched as possible. If an impeller with too larger diameter is used (as is the case with many hybrid turbos) the turbine will operate on the left side of the curve and will not achieve peak efficiency. With modern impeller design which tend to feature more backswept blades it possible to achieve optimal U/C with a slightly larger impeller however I would not recommend going below a turbine wheel to impeller diameter ratio of 0.8.
Note: The reason in most turbochargers the compressor is larger is due to mechanical compromising restricting the diameter of the turbine wheel.
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