Figure 24: P-Diagram for engine flow
SYSTEM AND SUPPLY CURVES
The pump characteristic curve (or supply curve) plots the pressure rise across the pump versus flow rate as the flow restriction across the pump is varied. This curve illustrates possible flow rate and pressure rise combinations that a given pump at a single rpm can supply. The pump characteristic curve is measured by connecting a variable valve to a pump and varying the valve position. This curve will tend downward as the flow rate increases, because the flow rate will increase as the restriction across the pump is decreased for a constant input in energy.
Similarly, the possible combinations of flow rates and pressure rise required by a system is illustrated with the system or demand curve which plots the pressure loss across the system through which the fluid is being pumped.
The system curve tends upward as the flow rate increases, because the frictional losses increase as the flow rate through the system is increased.
As illustrated in figure 25, the flow rate and pressure loss through a cooling system graphically intersect at the operating point for a given pump and system. The operating point is that point at which the flow rate and pressure rise provided by the pump is equal to the flow rate and pressure rise required by the system.
The operating point in this example is a stable operating point, because the supply curve has a more negative slope at the operating point than the system curve. This means that if there is a perturbation, and the flow rate is decreased, then the driving pressure supplied by the pump will exceed the pressure required by the system, and the flow will increase back to the operating point. In the following paragraphs, you will see that the system curve shown here is a simplification of the system characteristic curve of a fluid in a firing engine, and under these conditions unstable operating points are possible
Figure 25: Coolant Operating Point
While the engine is running, heat is transferred from the engine to the coolant by means of forced convection and sometimes by means of nucleate boiling at very high heat fluxes. After engine shut-down the heat is transferred away from the engine via coolant evaporation. Figure 26 shows the rate of heat transferred versus wall surface temperature for both nucleate boiling and forced convection
Figure 26: Pool boiling curve for water at atmospheric pressure[12]
Figure 26 shows the change in heat transfer mode as the surface temperature of the solid increases. The region from point A to point B is convective heat transfer. At a given velocity a small change in heat flux will result in a relatively large change in the solid surface temperature. The region from point B to point C represents the nucleate boiling regime. Here the wall temperature change is relatively
Noise Factors
Engine structure thermal properties (V) Wall thickness variation (V)
Engine load (U) Engine Speed (U)
Noise factor legend:
V = Component variability U = Customer Usage E = Environmental
Localized
Heat Flux Internal Flow Subsystem
Local Metal Temperature
Side effects Thermal stress
Failure Modes Unstable heat transfer Cavitation
Surface erosion Local coolant velocity
Surface area Coolant temperature
Coolant pressure Coolant thermal properties
Control Factors
Coolant flow rate (m^3/s) Operating point
Pump supply characteristic System resistance or demand curve
Pressure Difference (kPa)
B C
F
E
A
Velocity
D D'
Surface Heat Flux (W/cm^2)
Metal Surface Temperature (Log °C)
small as the surface heat flux is increased. Although this relative stability in the surface temperature is desirable, operating the cooling system in the vicinity of point D is risky. Point D is known as the critical heat flux, and it represents the point at which any increase in wall temperature will result in a decrease in the amount of heat transferred. If the heat flux increases beyond the value at point D, the wall temperature will jump from the surface temperature at point D to the surface temperature at point D’ (or higher). This excursion in surface temperature will generally result in the overheating of the solid surface, hence the term “burnout”, which is sometimes used to describe this condition. This decrease in heat flux beyond point D occurs because the very small vapor bubbles which are formed during nucleate boiling (which quickly collapse as they move away from the solid surface), have increased in size and energy to the point where they have begun to coalesce, and blanket the solid surface. The progression from convective heat transfer to film boiling is illustrated in figure 27.
Figure 27: The various stages in the pool boiling curve[9]
Critical Heat Flux (CHT) refers to the onset of vapor blanketing in an open channel, however in an engine, heat transfer takes place inside small diameter passages.
Vigorous nucleate boiling can lead to blocking of small diameter passages at a heat flux that is lower than the CHT observed in an open channel. When vapor blocking occurs in a closed passage, the presence of macroscopic bubbles can result in not only an insulation of the solid surface, but also a blockage of the incoming coolant flow.
Refer to Figure 25, which showed the system curve when the fluid is a single phase liquid and the passages are not heated. If a single phase gas were used, the curve would be steeper, representing a greater pressure loss for a given flow rate.
Figure 28 shows two phases present in a heated passage.
This two-phase curve represents the flow characteristics of coolant in a running engine.
Figure 28: Flow characteristics of coolant in a running engine
Onset of Flow Instability (OFI)
The onset of flow instability (OFI) occurs on the two-phase flow curve at the local minimum where the curve begins to turn upward. At this point the flow rate in the engine coolant passage falls below a critical flow value. The vapor bubbles begin to block the flow of coolant to the extent that an increased driving pressure is required to maintain flow.
At a flow rate that is below OFI, the slope of the system curve is more negative than the supply curve. This situation is always unstable as illustrated in the following scenario.
In the system represented by the above curves, the system curve crosses the supply curve at points A, B, or C. If the flow rate falls below OFI, the system must operate at point A or point B, however at point B, any reduction in flow would result in an increase in pressure drop required, A-B Natural
convection
B Onset of nucleate boiling
B-C Nucleate boiling low heat fluxes
B-C Nucleate boiling high heat fluxes
C Critical Heat Flux
D-E Transition boiling
E-F Film boiling
Pump or supply curve Single
phase - gas
Single phase - liquid C Two phase flow
B A
Volumetric coolant flow rate OFI
Pressure difference across heated passage
which the pump cannot supply, and so the operating point would move to point A which represents all-vapor. Under these conditions the engine would overheat.
The system design must supply a flow rate that is well above the critical flow rate to avoid the onset of flow instability.
VERIFICATION
Detecting Flow Instability
To detect the onset of flow instability in an engine, run the engine in a dynamometer at the maximum heat rejection condition anticipated during vehicle operation, then slowly decrease the flow rate through the engine. On a vee engine, this best done by reducing the flow on only one bank at a time. When conducting this test it is necessary to devise a test set-up where the engine ignition can be shut off, and the flow rate rapidly increased when the critical flow rate is reached, to minimize the possibility of damage to the engine due to overheating.
The critical flow rate is reached when the flow rate becomes unstable, and the volume of the coolant increases (if the coolant temperature is held constant during testing).
This critical flow rate is a function of heat rejected to the coolant, and the amount of subcooling at the engine exit or inlet.
Subcooling refers to the amount of temperature difference between the boiling point and the temperature of the fluid.
When a liquid is lower in temperature than its boiling point, it is sub-cooled. For example when water is at 95 degrees C, and atmospheric pressure, then the water is at 5 degrees C of subcooling. The closer the temperature of the exiting coolant is to boiling, the higher will be the critical flow rate (see figure 29).
Figure 29: Critical flow rate vs. subcooling for a hypothetical engine
For new engines, the trend among engine manufacturers is to provide flow rates that correspond to an entirely convective heat transfer mode, with no excursion into the nucleate boiling mode. The advantage of this approach is that there is no danger of approaching OFI, which cannot as yet be analytically predicted. Furthermore, these high velocity cooling passages are smaller in cross-section, so the total fluid in the engine is reduced. This decreases the time required to heat up the coolant and therefore improves passenger compartment warm-up. In order to assure that the heat transfer within the cooling passages remains safely within the convective heat transfer mode, the local coolant velocities must be matched to the local heat flux so that a relatively constant surface temperature is maintained throughout the engine. This is sometimes called “precision cooling”. Computational fluid dynamics (CFD) is used to determine local flow velocities, and finite element models are used to determine local heat transfer rate.
Decreasing Minimum Flow
If the minimum flow test indicates that the engine required minimum flow is close to or greater than the supplied flow rate, then the cooling system designer must increase the flow rate to the engine, or decrease the bulk coolant temperature. However if the engine design is under development, or is undergoing a change which will require new tooling, then any changes to the engine that will decrease the required coolant flow should be considered.
These changes generally consist if increasing flow velocities at locations of relatively low flow and high heat flux.
CFD is often used to determine these areas of low coolant flow velocity. Magnesium borate has also been used as a means of determining the location of coolant vaporization.
Magnesium borate is a substance that can be added to the coolant during an engine dynamometer test, which will deposit on the metal surfaces at locations of boiling and high coolant temperatures. The test engine is then cut apart, to observe the locations in the cooling passages where the magnesium borate has been deposited.[13]
0 5 10 15 20 25 30
0 20 40 60 80
Exit subcooling (degrees C) critical one side flow (liters/min)
(Exit subcooling = Boiling temperature minus the coolant temperature at engine outlet)
OVERVIEW
This chapter discusses:
• coolant flow requirements for the heat exchangers and degas reservoir,
• system design alternatives,
• and verification methods.
TERMS USED IN THIS CHAPTER
Loss coefficient: The non-dimensional difference in pressure across a component
Cavitation: Cavitation occurs when the pressure at a point within the fluid falls below the saturated vapor pressure causing the fluid to locally boil. Vapor bubbles form and subsequently collapse as they are carried into regions of higher pressure or lower temperature.
COOLANT FLOW REQUIREMENTS
Figure 30 shows a parameter diagram for the external flow subsystem
When existing production components are used, system design begins by determining the flow requirements of the components.
Figure 30, P-diagram for flow to components
HEAT EXCHANGER FLOW REQUIREMENTS
A typical fin and tube heat exchanger performance curve is shown in Figure 31. Note that the curve is steep at low flow coolant rates, and is flat at high coolant flow rates. At low flow rates large gains in performance can be achieved with small increases in flow rates.
For radiators and heaters the program targets for flow rates must be determined by a cost benefits analysis, considering the following:
• the cost of increased coolant and/or air flow rates,
• cost and weight of larger radiators, and larger radiators,
• and the consequences of increased coolant temperatures.
Most heat exchangers will have some limitation on the maximum flow rate that can be tolerated. Excessive flow rates can lead to erosion damage of the heat exchanger tubes.
The cooling system must provide flow to the radiator, heater, engine, and any other heat exchangers in the coolant circuit at a rate which is adequate for performance, but does not exceed the flow rate that will cause an unacceptable amount of erosion. This requirement must be met under all operating conditions, for all customers, throughout the life of the vehicle
Noise factors Pump assembly (V) Gasket variation (V)
Deposit (A) Heat exchanger fouling (A) Loss of thermostat stroke (A)
Engine speed (U) Vibration (E)
NPSHA (E) Trapped air (E)
Pump geometry Pump Ratio
Component hydraulic resistance Control Factors