# Supercharger Thermodynamics: Impact of Coolant Flow Rate on Intake Air Temperature

Introduction

Forced induction is an excellent means for increasing the volumetric efficiency and power output of internal combustion engines. There is, however, a penalty for compressing intake gases prior to combustion in the form of added thermal energy (heat) to the air stream. As the compression ratio through the air mover increases, the amount of mechanical work performed on the air also increases. In addition to the isentropic flow limits of compressed gases, the inefficiency of the air mover itself (primarily in the form of blade slip and friction losses) is added to the air stream as heat. The thermal energy added to the air stream will increase the temperature of the air proportionate to the mass flow rate of the incoming air.

In the proceeding series of short technical articles, the goal is to provide some fundamental insight into predicting heat input from various compressor operating conditions and an abbreviated education on the heat transfer theory behind managing the resulting Intake Air Temperatures (IATs). A thermal resistance network for a typical compressor coolant loop has been constructed to serve as the foundation for all future discussions on how to improve IATs.

The focus of the present article is on the impact of liquid coolant flow rate on Intake Air Temperature (IAT). Increasing water flow rate in a supercharger coolant loop always increases the cooling capacity of the system which will, in turn, reduce IATs. There are, however, costs associated with increasing water flow rate: the capital expense of purchasing higher flow water pumps and the parasitic power draw required to operate the pump at the elevated flow rates. The topic of coolant flow rate and the power draw required to move water as a function of flow rate and flow impedance will be covered in Part 2 of this series. After reading the first two articles in this series, the goal is to be able to identify a targeted coolant flow rate based upon the optimal balance between performance gain and the economic and parasitic power loss of higher flow rates.

An analytical model has been constructed to demonstrate both the enhancement in thermal performance and eventual diminishing return of increased coolant flow rates. The relative significance of each contributing thermal resistance in the supercharger coolant network will also be presented.

Supercharger Coolant Loop

Figure 1 below shows a quick illustration of the fundamental components within a supercharger cooling loop. Air is drawn through the cold air intake and into the engine by the compressor (supercharger) creating negative pressure on the upstream side of its internal blades. As air passes through the compressor, the blades perform mechanical work on the air volume which increases the pressure and temperature of the air volume. Conductive heat transfer through the compressor housing also increases the temperature of the passing air through the system.The high pressure and temperature air then passes through an intercooler which serves as an air to liquid heat exchanger (h/x). Cool liquid passing through the intercooler absorbs heat from the air stream and transports the heat to an external liquid to air heat exchanger (radiator). Heat from the liquid coolant is absorbed by ambient air passing through the heat exchanger.

Fundamental Law: Energy is conserved – meaning that for a steady state system, energy in equals energy out. In the case of the simplified supercharger coolant loop, heat rejected from the air stream (thermal energy) at the intercooler *will always be equal* to the heat absorbed by the ambient air at the heat exchanger. There are caveats to this, particularly in the form of under-hood heat producers contributing to the temperature rise of the coolant, but they are, for the purposes of this discussion, considered to be irrelevant.

Fundamental Law: Thermal Energy (heat) will always transfer in the direction of high temperature to lower temperature. Anytime there is matter in contact at a dissimilar temperature, heat will be transferring from the warmer substance to the cooler substance. *The greater the temperature difference between hot and cold matter, the greater the quantity of heat that will be transferred between the two volumes*.

Now that we are aligned on the energy transport path, its direction of flow, and the impact of temperature difference, we can discuss the impact of thermal resistance (or the impedance to heat transport) on temperature difference between a hot and a cold volume. Many people find the analogy to electrical resistance an effective tool to conceptualize thermal resistance. This is a completely valid approach and is presented here. In this analogy, temperature gradient (or difference) between a high and a low temperature volume creates the ‘heat transport potential’ or “voltage”. The thermal resistance is analogous to electrical resistance and heat flow (in units of Watts or BTU/hr) is analogous to current flow through the resistor. The common equation for electricity can be related to heat transfer as below:

Where is the flowrate of heat and represents the temperature difference between the hot and cold volume. The units of thermal resistance () are degrees of temperature difference per unit of heat flow (°C/Watt or °F/(BTU/hr)). As the equation suggests, as the thermal resistance increases, so must the temperature difference in order to transport the same amount of heat. Figure 2 below shows the 1-D thermal resistance network for the simplified supercharger cooling loop where the sum of R1, R2, R3, R4, R5, and R6 are combined into a single equivalent resistance shown as “Rtotal” in Figure 1. *In order to reduce Intake Air Temperatures, the goal is to reduce the total thermal resistance from supercharger discharge to the ambient air as much as possible.*

While it is not important to understand the specific physics behind each thermal resistance in this network, there are a few key takeaways that should be noted. Here are the most critical pieces of information pertaining to this topic:

The variable

*A*represents the surface area of each respective component in the thermal resistance network and is in the denominator of each thermal resistance equation. This means that as surface area increases, thermal resistance decreases.The variable

*k*is the thermal conductivity of the respective component material. Material choices*do*matter, but switching from a decent thermal conductivity material such as aluminum to one with amazing thermal conductivity such as copper only provides an incremental improvement in thermal resistance as the material conductivity only exists in 2 of the 6 resistance equations.The variable

*h*is the overall heat transfer coefficient. There are many variables that impact the overall heat transfer coefficient, but, in forced convection for a given fluid, the most significant influencer is flow velocity. Again, being in the denominator of most of the thermal resistance equations,**increasing flow velocity will increase heat transfer coefficient and reduce the thermal resistance of that component.**Each individual resistance is stacked in series with the rest of the network. Reducing one resistance will reduce the total thermal resistance, but even completely eliminating a resistor will not bring the total resistance value to zero. What this means is that even if the external heat exchanger were grown to be the size of a football field with surface area effectively approaching infinity and its resistance value going to 0, the remaining resistors in the network remain unchanged. At some point, reducing one resistance value ceases to have a significant impact on the overall total thermal resistance.

Now that we have become familiarized with the heat transport path, the impact of thermal resistance on heat transfer, and the nature of the thermal resistances within the flow network, the final step is to use a real supercharger coolant loop as an example to demonstrate the relative contribution of each independent resistance to the overall total thermal resistance.

**EXAMPLE 1**

**Initial Conditions**:

Tambient: 30°C (86°F)

Tsc_discharge: 121°C (250°F)

Engine Airflow: 800 CFM

Vehicle Speed (reflecting air speed through external heat exchanger): 40 MPH

**Coolant Flow rate: 10 GPM**

**External Heat Exchanger**:

Width: 25 inches

Height: 11 inches

Depth: 3.125 inches

**Intercooler**:

Width: 7 inches

Height: 4.5 inches

Depth: 4.5 inches

Figure 3 above shows the previously discussed 1-D thermal resistance network with the respective resistance values overlaid as they relate to the conditions in Example 1. Values shown are in units of °C/Watt and have been multiplied by 1000 to clean up some of the decimals. There are a couple of quick observations to be called out:

The conduction resistances are quite small compared to the water and air-side thermal resistances

The intercooler air-side resistance dwarfs most of the other resistances in the stack

Besides the intercooler air-side resistance, at 10 GPM system coolant flow rate, the water-side convection thermal resistances are the next biggest offender - comprising roughly 19% of the total thermal resistance. To illustrate the impact of flow rate on this thermal resistance, Figure 4, below, shows the same heat exchanger and intercooler setup as Example 1, but with a Coolant Flow Rate of 3 GPM. Notice that the total thermal resistance has increased by nearly 28% and the contribution of the water-side thermal resistance has grown from 19% to 38% of the total thermal resistance stack.

To further illustrate the impact of water flow rate on overall thermal performance of the supercharger cooling loop, Figure 5 below was constructed using numerical modeling software. The blue line shows the intake air temperature for the conditions listed in Example 1 as a function of increasing coolant loop water flow rate. As can be seen, there is a strong dependency on water flow rate at lower flows, but there does come a point where the reduction in water-side thermal resistance becomes less significant to the total thermal resistance. At this point, diminished returns on increasing water flow rate are observed.

By now, it has been made clear that thermal resistance decreases with increases in flow rate. That trend, however, as mentioned, is asymptotic – meaning that greater flow rates start to yield smaller and smaller improvements in performance. Figure 6, below, shows the thermal resistance curve for the total coolant loop described in Example 1 as a function of flow rate. Additionally, the graph in Figure 6 also shows the respective individual thermal resistances for both the intercooler and the external heat exchanger. Not surprisingly, the intercooler thermal resistance is significantly larger than the external heat exchanger due to relative size difference.

The asymptote region of the thermal resistance vs. flow rate curve represents the point at which the water-side thermal resistance is no longer significant in the total thermal resistance of the system. This region is commonly referred to as ** fully saturated flow**; a term which can be applied to both the water and air portions of the thermal resistance network. Figure 6 below shows how close the system in Example 1 is to operating at fully saturated water flow conditions at various water flow rates. In this example, the system is 90% saturated at 21.5 GPM. Increasing water flow much beyond this point will have limited value.

Understanding the impact of water flow and saturated flow conditions for a supercharger cooling loop is helpful, but it is not trivial to determine the operating flow rate at which the water-side thermal resistance can be considered fully saturated. Determining this value requires unique knowledge of the geometry of each component within the cooling loop – particularly as they pertain to the transition from laminar to turbulent flow within the heat exchanger microchannels. There is, however, two guiding principles that can be applied:

*Larger volume heat exchangers require greater water flow rates to reach flow saturation**Greater air flow rates through the heat exchanger require greater water flow rates to reach water flow saturation**Heat exchanger flow paths in parallel yield more return for increased water flow rate than those that are in series (longer tube lengths) for the same total volume. This is due to reduced velocity through the liquid channels.*

In order to help our readers determine the water side flow rate they should be targeting for a particular heat exchanger setup, the data in Table 1a and 1b below shows the 90% fully saturated flow rate for a range of heat exchanger sizes using a generic louvered fin, dual-pass, heat exchanger construction. These results are calculated assuming a 20 MPH flow velocity through the heat exchanger which would be common for many high performance fans. As can be observed from the tables, the target flow rate for a given heat exchanger depends heavily upon the size of the unit.

*Please note: these results are based upon a generic system using numerical modelling and may not accurately reflect your heat exchanger characteristics. They are not intended to be specification for any manufacturer’s heat exchanger product but, rather, a guideline for typical system design targets.*

Conclusions

Hopefully the preceding discussion on the supercharger coolant loop thermal resistance provided some usable insight into future forced induction projects. Below are the critical pieces of information that the reader should walk away with from this article:

The thermal resistance of the intercooler and the external heat exchanger add together in series with several other thermal resistances to combine for the total thermal resistance of the supercharger coolant loop.

The total thermal resistance between the supercharger discharge and external ambient air dictates the downstream IAT. Lowering this thermal resistance will reduce IATs.

Increasing the water flow rate of the coolant loop will decrease the water-side convection thermal resistance in both the intercooler and the external heat exchanger. Because the resistance of those two components adds together in series and the water flow rate is constant throughout the loop, the impact of water flow rate can be quite significant.

There is a point in which the water to fin convective thermal resistances of both the intercooler and external heat exchanger are no longer a significant contribution to the sum total thermal resistance which yields a diminished return for increasing this value. This is referred to as

*fully saturated flow*.The point at which the benefits of increasing water flow rate show diminished return depend heavily upon the geometry and air flow rate of the intercooler and the external radiator, but the single best indicator is the size. Smaller heat exchangers transition to turbulent flow faster and thus see diminished return (or flow saturation) at lower flow rates.