Efficient Volvo Bus Cooling System,Using Electrical Fans: A comparison between hydraulic and electrical fans

Efficient Volvo Bus Cooling System, Using Electrical Fans

A comparison between hydraulic and electrical fans

RITA BAIL˜ AO MARTINS FERNANDES

Master’s Degree Project

Stockholm, Sweden June 2014

Abstract

Economical and environmental factors together with energy policies towards more efficient sys- tems are the driving force for the development of the vehicle industry. Significant changes have been made to fulfill new emissions legislation but the basic internal combustion vehicle architecture has been kept. New emission treatment systems that increase the thermal loading of the cooling system had been added within the same package envelope as before, which means less space to place cooling fans and a greater need for airflow. Changes in the cooling system, namely the replacement of the hydraulic fan drive system by electrical fans is one of the energy efficient alternatives for several city buses under certain environments, like the ”typical red city buses”, well-known in the United Kingdom. In this thesis study, hydraulic fans are compared with electrical fans and a road-map of the benefits and drawbacks of the two systems is developed, based on real traffic performance performance data and the results of existing simulations and tests. In addition, new simulations are presented in order to find the most efficient design for the cooling system as well as a comparison of these results with previous ones. This road map will be used later by Volvo-Buses Group as a tool to better understand in which circumstances electrical fans can be beneficial, in terms of fuel consumption, noise production, cooling performance, control of the fans and associated costs.

Keywords : hydraulic fan cooling system, electrical fan drive system, radiator, fan efficiency, fan shroud, static pressure, oil cooler, charge air cooler, built-in-resistance.

Part I

Preface

Dear reader of this thesis. This master thesis project is the final sign off of the last year of my master of science. It is based on engineering reports made by Volvo engineers, scientific articles and simulation results from Volvo GTT and Volvo Buses. The research was carried out from later January 2014 to July 2014, and presented in the end to Volvo AB and to KTH (Royal Institute of Technology), in Stockholm.

The topic was based on the company’s request to analyze the current options for the fans of the bus cooling systems and to better understand electrical fans in terms of cooling performance. The master thesis project was carried out by Rita Fernandes as an intern, Reza Fakhrai as supervisor at the university Christer Kjellgren as supervisor at the company. The project was financed by the AB Volvo, namely by the department of Powertrain Development and conducted by the Cooling System group, with Charlotte Eldh as the line manager. The empirical research took place in Volvo Buses offices in Gothenburg, mostly located in Arendal. All of the co-workers: Chirster Kjellgren, Erik LindÃľn, Joel SÃűrborn, Eva BjÃűrk, Peter Gullberg, Erik Dahl, Dalibor Cuturic, Jessica LexÃľn, Stephan SchÃűnfeld and the remaining group are highly appreciated for their help and availability during the thesis work. Moreover the input from all the interviewees was crucial and without it, there would not be the possibility to get so quickly the results of this thesis. Also a special thanks to my friend Andrea who helped to feel home in this new city of Gothemburg and my Portuguese friends who guided me through all the aerodynamics concepts.

It has been very nice to get to know you, and I hope to continue to learn more from you. Francisco, thanks for helping me with proper English. Finally, I would like to thank my family and all of my friends for their warm and kind support. At the end of the day, you have always been there for me. Thank You.

Confidentiality clause Due to confidentially reasons, all the parts with sensitive information were deleted form this report. This includes all the tables, figures and graphs with valuable content for Volvo AB. A different and complete report of this thesis was delivered to Volvo AB, as well as a shorter version with the main results and recommendations.

Gothemburg, July 2014 Rita Fernandes

Contents

I Preface 2

II Introduction 8

III Objectives 9

IV Volvo Buses and cooling system 10

1 Thermodynamic and Heat Transfer fundamentals 10

1.1 Conduction . . . 10

1.2 Convection . . . 11

2 Bus Cooling System 11 2.1 Fan Systems . . . 12

2.2 Radiator . . . 13

2.3 Engine water pumps . . . 14

2.4 Charge air cooler . . . 15

2.5 Oil cooler . . . 15

2.6 Fans shroud . . . 15

2.7 Thermostats and other sensors . . . 15

2.8 Header Tank and Recovery System . . . 16

3 Hydraulic Fans 16 3.1 Coolant Temperature Sensor . . . 16

3.2 Hydraulic pump . . . 16

3.3 Pump control plate . . . 17

3.4 Control valve and check valve . . . 17

3.5 Hydraulic fan motor . . . 17

4 Electrical Fans 17 4.1 Radial, Axial fans and Diagonal fans . . . 19

4.2 How to select the right fan . . . 20

4.2.1 The total cooling requirements . . . 21

4.2.2 Static pressure . . . 21

4.2.3 Total System Resistance / System characteristic curve . . . 21

4.2.4 System Operating Point . . . 22

4.2.5 Stall effect and instability regions . . . 22

4.2.6 Efficiency of electrical fans . . . 22

V Modeling and analyzing electrical fans 23

5.2 Fan Laws . . . 23

5.3 Influence of density . . . 24

5.4 Impact of Fan Diameter . . . 24

5.5 Series and Parallel Operation . . . 25

5.5.1 5 SPAL electrical fans (305 mm) vs 2 SPAL electrical fans (405 mm) . . . 28

5.6 Blade angle . . . 28

5.7 Distance between fan blades and fan ring . . . 28

5.8 Voltage imposed and consequences in fan curves characteristics . . . 28

5.9 Possible fan suppliers . . . 31

5.10 Pusher Fans vs. Puller Fans . . . 31

6 Evaluation of an electrical cooling system: London buses case: B5LH (hybrid) and B9TL 34 6.1 Exhaust gas recirculation (EGR) . . . 34

6.2 Real Data taken from Volvo Data Base (LVD) . . . 34

6.3 LAT and IMTD . . . 34

6.4 Derating . . . 35

VI Simulations and Tests 36

7.2 AMESim . . . 36

7.3 Input Data . . . 37

7.4 Implementation . . . 37

7.5 Built-in-resistance . . . 37

7.6 Effect of removing the oil cooler . . . 39

7.7 Cooling performance: LAT and IMTD . . . 40

7.8 Separated CAC and radiator installation . . . 40

7.9 Effect of the fan shroud . . . 42

8 Coaches cooling performance using electrical fans 44 8.1 Cooling performance: LAT and IMTD . . . 44

VII Conclusions 45

VIII Recommendations and future work 47

List of Figures

1 Scheme of bus cooling system heat exchangers, air flow direction and respective pressure

differences . . . 12

2 Scheme of a turbocharger.Adapted from [39]. . . 13

3 Scheme of a water pump. Adapted from [42]. . . 14

4 Scheme of hydraulic valves . . . 17

5 The effect of multiple fans on system pressure and flow rate. Adapted from [3]. . . 20

6 Change of static pressurer . . . 21

7 Sketch of fan and system curve. Adapted from [3] . . . 22

8 Stall: unstable zone in the fan curve . . . 23

9 Effect of an increase in fan diameter in air flow and static pressure . . . 25

10 The effect of multiple fans on system pressure and flow rate . . . 26

11 Lower duct pressure due to fans placed in series . . . 26

12 5 fan curves in a parallel configuration, with a diameter of 305 mm and 3750 rpm speed . 27 13 2 fan curves in a parallel configuration, with a diameter of 450 mm and 3750 rpm speed . 27 14 Different fan curves for the same system resistance . . . 28

15 A comparison between 2 real SPAL fans versus 5 small SPAL fans . . . 29

16 Dependency between pressure drop and blade angle. Adapted from [3]. . . 29

17 Fan ring location in the cooling module. Adapted from [3]. . . 30

18 Dependency between pressure drop and blade-ring distance. Adapted from [3]. . . 30

19 Effect of voltage in fan performance . . . 31

20 Sound level for different electrical fans . . . 33

21 5 electrical fans model: Heat stack (radiator and CAC) connected to 5 electrical fans . . . 38

22 Heat module: CAC, oil cooler and a radiator in the backside . . . 39

23 CFD calculations: case a) without oil cooler and case b) with oil cooler . . . 40

24 LAT change versus fan speed . . . 41

25 IMTD versus fan speed . . . 41

26 CFD model with fans . . . 42

27 CFD model without fans . . . 42

28 Different EBMpapst fan combinations . . . 44

29 Radiator performance curves for different coolant flows . . . 45

30 Different fan curves for coaches and operating points . . . 46

Nomenclature

∆p Static pressure drop (Pa)

˙m mass flow (kg/s) A surface area (mˆ2)

AM ESim Advanced Modelling Environment for Performing Simulations of Engineering Systems AV Volumetric flow (m³/s)

B5T L Hybrid bus model with 5L cylinders B9T L Bus model with 9L cylinders BiR Built in Resistance (-) CAC Charge air cooler

CF D Computational Fluid Dynamics

cp Specific heat at constant pressure (J/(g.K)) D Fan diameter mm

E Total energy of the system (J) e Flow energy (J)

EBM papst Germany fan supplier EGR Exhaust gases recirculation g Gravitational constant (m/s²) GT T Volvo Group Trucks Technology H Blades shape factor (dB)

h Heat transfer coefficient ([W/m²K]) ICE Internal combustion engine

IM T D Intake manifold temperature difference (℃) Lw Sound power level (dB)

LV D Logged Vehicle Data Analysis Tool

P Power (W)

p Total pressure (Pa) pD Dynamic Pressure (Pa) P W M Pulse-width modulation Q Heat transferred (J)

qspecif ic Specific Heat of the Radiator (kW/K) RAD LOW Radiator type used for City-Buses RAD W IDE Radiator type used for Coaches Re Reynolds number (-)

rpm Revolutions per minute SP AL Italian fan supplier Tf Fluid temperature (℃) Ts Surface temperature (℃) T T T Top tank temperature (℃) u Fan tip speed (m/s) V Fluid velocity (m/s) V BC Volvo Bus Corporation W Sound power (W)

W Work done on the system (J) W0 Reference sound power z Height (m)

Part II

Introduction

The improvement of the thermal management of a vehicle can contribute significantly to reducing emis- sions and lower fuel consumption. The demand for cooling power varies greatly with the surrounding environment. Under certain conditions, wherein the climate is not too adverse and the city’s topography is smooth enough, the cooling demand is much lower than a situation where the topography is rough and the climate is hot. Electrical fans represent a good solution for climates where the cooling demand is lower since they can work at lower speeds and are almost totally independent from the engine speed.

When used on many auxiliary applications, electrical fans can provide additional air flow to prevent overheating, supplement the existing belt-driven fan as a new means to control unacceptable noise levels and aid in the redesign of the engine compartment by relocating the heat exchangers. This leads to the central question of this thesis:

Are electrical fans the best option when compared to hydraulic fans, for the same cooling performance demand?

The immediate answer seems to be positive since electrical fans consume only 2 kW and hydraulic fans consume up to 25 kW (for their maximum speed). This represents 12.5 times more power consumption, even idling or operating at lower speeds. This is due to several reasons, and the aim of this thesis is to explain and compare the two solutions, with a simple 1D model, (in steady state conditions), together with the results of several previous simulations and tests, done during the past 10 years by Volvo Group engineers. It is important to understand how both systems behave when varying the heat load, fan speed, air flow, coolant flow, etc, over time and also what happens if one introduces changes in the system configuration, namely when changing the fan shroud, the consequence of removal of the oil cooler used by the hydraulic system and also to analyze the changes in static pressure if one splits the radiator and the charge air cooler. Thus, the scope of this thesis is to better understand the difference in power consumption and cooling performance of a cooling system moved by a hydraulic fan and another, moved by electrical fans. To do that, the city-buses and coaches are used as case-studies. For the city-buses, two different bus models were selected: B9TL and B5LH. B9TL is basically a 9L engine, typically used in London and known as the London red city-buses. This model was recently replaced by a B5LH, (5L engine). Every once in a while, vehicle manufacturers have to make changes regarding emissions and fuel consumption [34], since there are rules made by the European Union which state the maximum temperatures allowed in the different parts of the engine system in order to control the emissions of NOx, total hydrocarbons, particulate matter and COx. They are known as the European Emission Standards:

Euro 5 and Euro 6. Euro 6 was implemented in 31th December 2013 for buses and trucks. B5LH is an hybrid bus that in Euro 5 use a hydraulic fan and in Euro 6 electrical fans. Although the engine is different for the two emission standards, it is interesting to compare this model.

Part III

Objectives

The objective of this thesis is to find possible fan cooling systems configurations and to better under- stand why electrical fans are advantageous compared to hydraulic fans. The first step is a literature review about the bus cooling system, in order to find a definition of cooling performance and thus to discover what is limiting electrical fans, by studying the different types of fans and respective suppliers, the possible system voltage and configuration. The background analysis consists in the analysis of the LVD, a Volvo database that keeps tracking the vehicles’ performance in real time each time they go to service. They represent the data in real traffic conditions and several variables can be chosen including the fuel consumption, the voltage, cooling capacity, fan clutch type, fan speed and engine speed. To- gether with the real values of such variables, a 1D model using AMESim software package is used. The constructed steady-state model should be useful to evaluate different heat transfer parameters of the whole system. These simulations will then be used for other VBC future projects since they will allow to reach conclusions related to the consequences of switching to electrical fans, namely in what concerns fuel consumption, the optimized number and configuration of the electrical fans, cooling performance, noise, product cost, powertrain performance and ventilation of engine compartment. Some CFD calculations are also performed in order to reach conclusions related to the configuration of the system, namely in what concerns the disposition of the charge air cooler and the radiator, since due to spacial constraints, they are in a sandwich configuration. The cooling performance gained if they are placed side by side was not so far calculated; a measurement of the engine bay temperature was the only study done at the time this thesis was written, with a gain of 20℃, though with sandwich configuration using hydraulic fans and split configuration using electrical fans. CFD is also used to measure the velocity of the air through the radiator’s surface, since the cooling performance depends also on that together with the built-in-resistance.

Part IV

Volvo Buses and cooling system

This chapter provides a brief description of Volvo Buses. Volvo Buses offers a broad range of passenger transport solutions to match the diverse customer demands. The product offer can be classified into three segments: city, commuter and coaches. This thesis will analyze the cooling system of city-buses and coaches.Volvo Buses has a relatively small business and restricted budgets so it cannot afford to run standalone process development efforts. However, the business scenario is rapidly changing with the introduction of emerging economies in Asia and South America, which have different requirements on products than their European counterparts and the strategy of adapting European products to these countries is no longer a feasible idea since the environmental conditions are most part of the times considerable different.

1 Thermodynamic and Heat Transfer fundamentals

The engine cooling system from a perspective of heat transfer, can be summarized in three points.

• Heat transmission from engine to engine coolant

• Engine cooling circuit, that transports the heat from the engine to the heat exchangers (radiator and charge air cooler)

• Dissipation of heat from the hot coolant into the ambient air through forced convection

According to the second law of thermodynamics, if an isolated system is not in equilibrium, its entropy will tend to increase over time, until it reaches an equilibrium for its maximum value. This means that its energy disperses over time, and less energy is available to do useful work. On the other hand, according to the first law of thermodynamics, energy cannot be destroyed and it changes from one process to

another. Z

dE=I

∂Q − I

∂W (1)

Exergy is the term used to describe the destroyed energy when a process involves a temperature change, which is proportional to the entropy increase of the system and its surroundings. Heat cannot flow from a material at lower temperature to a material at higher temperature spontaneously. It is necessary to provide energy for that to happen, either by work or heat. For a cooling system, heat at a lower temperature is worth more than heat at a higher temperature. Therefore, the efforts are in the direction of cooling a flow with another flow that is as close in temperature as possible. Whenever there is a temperature difference in a medium or between media, heat transfer must occur, either by conduction, convection or radiation. Conduction can occur between solids or a stationary fluids, convection from a surface to a moving fluid and in radiation heat exchanges between two surfaces. Since the majority of the materials present in the cooling system are made of aluminum, iron and other materials with lower emissivity coefficient, ε, radiation transfer is neglected in this study, since according to the Stefan- Boltzmann Law, it is dependent on the materials emissivity. (even if the emissivity coefficients for some materials vary with the temperature.)

1.1 Conduction

Energy is transferred on a molecular scale and no movement of macroscopic matter relative to one another. The energy transfer occurs by interaction of particles more energetic to less energetic ones.

This net transfer of energy by random molecular motion is called a diffusion of energy. This also occurs in liquids but molecules are more closely space. In solids the conduction is due to lattice vibrations.

Fourier’s law represents the relation between the time rate of heat transfer through a material and the temperature gradient of a certain area, through which the heat is flowing. This law can be expressed by the differential and integral form. The differential form of Fourier’s Law of thermal conduction shows that the local heat flux, Q, is equal to the product of thermal conductivity, k, and the negative local

temperature gradient, −∆T . The heat flux density is the amount of energy that flows through a unit area per unit time.

Q= −k∆T (2)

In Equation 2 Q is the local heat flux (W), k is the material’s conductivity (W Kˆ-1), and ∆T is the temperature difference (K). The thermal conductivity of a material generally varies with temperature, thus, k is a measure of the rate at which heat flows through a given material. It is measured by the amount of heat, Q, that flows through the material of a thickness, dx, per unit of temperature difference,

∆T For many simple applications, Fourier’s law is used in its one-dimensional (1D) form [29]. For instances, in the x-direction,

qx= −kdT

dx (3)

unit

1.2 Convection

Convection occurs due to temperature differences between a fluid and a solid boundary. Due to the fluid motion redistribution of energy partly happens due to conduction. If the motion is due to an external device, like a fan in the case of an engine cooling system, it is called forced convection. In the other hand if the convection is due entirely to density gradients in fluid it is called natural convection. Heat transfer through convection is governed by Newton’s Law of Cooling [56].

Convective Heat Flux q = h(Ts− Tf) (4)

Convective Heat Transfer Rate Q = hA(Ts− Tf) (5) The area A is the surface exposed to the convective heat transfer, Tsis the surface temperature and Tf

is the fluid bulk temperature. The convective heat transfer coefficient h[W/m²K] will vary for different flow regimes (i.e. laminar or turbulent flow), fluid properties and temperature differences. Forced air coolers and heaters are examples of equipment that transfer heat primarily by forced convection. When a fluid flows over a flat plate, a boundary layer forms adjacent to the plate. The velocity of the fluid at the plate surface is zero and then increases to its maximum value just past the edge of the boundary layer. This boundary layer formation is important, since the temperature change from plate to the fluid (thermal resistance) is concentrated there. Where the boundary layer is thick, thermal resistance is higher and the heat transfer coefficient is small. At the edge of the plate, the boundary layer thickness is theoretical zero, and the heat transfer coefficient is infinite.

2 Bus Cooling System

The bus cooling systems plays two roles: the first is to make fuel efficient engines and the second in this context is that the cooling systems constitutes a loss. Internal combustion engines generate mechanical power by the energy generated by the heat flows in the engine compartment. As like any other machine, the efficiency of the engines is not unitary, so more heat has to come to the engine than what would be required if the process was isotropic. The outcome difference is waste heat that has to be removed in order to keep the components working at its designed conditions, avoiding that the lubricants and oil burn. This excess heat is also used to run the turbo-compressor. Thus, internal combustion engines remove heat through the hot exhaust gases, through cool intake air and mainly, by the cooling system.

A typical bus cooling system is composed by several components that differ to a system that is driven by one hydraulic fan or multiple electrical fans. The main components that are common to both systems are the charge air cooler, the radiator, thermostats and thermocouples, valves and pumps. Nowadays the cooling system is mounted in the rear of the vehicle due to space requirements. Previous studies also concluded that the cooling performance for the rear mounted installation is favorable compared to the front mounted cooling package. This was mainly due to the low vehicle speed, the high fan speed and to fewer obstacles around the cooling module resulting in a lower system restriction within the installation.

A radiator is basically a set of heat exchangers where the material that cools the engine (the coolant)

Figure 1: Scheme of bus cooling system heat exchangers, air flow direction and respective pressure differences

passes by when its temperature reaches a certain value. This value is measured by a thermostat located near the engine. When the coolants arrives into the radiator, with an initial temperature of 90 ℃, its temperature lowers due to the heat transfer from the outside air that passes firstly by the charge air cooler and finally by the radiator. This air flow is originated by the movement of the fans that pull the ambient air. Thus, in summary, the cooling system of a bus is a sandwich of a charge air cooler, an oil cooler, a radiator and fans [59].

The reason why there is a charge air cooler (or intercooler) is because buses have a turbocharger that needs also cooling. A turbocharger is a very complex mechanical system that increases the efficiency of fuel combustion by increasing intake air charge density through nearly isobaric cooling. A turbocharger helps to supply air by forcing it into the combustion chamber making the combustion more efficient.

Exhaust gases, normally at 220 ℃[7],[60] are channeled through the turbine housing where they increase speed. The gas then flows through the turbine wheel where it slows down again, releasing energy. The turbine wheel drives the common shaft that connects it to the compression wheel. The compressing wheel is driven by ambient air into the compressor housing, raising both its pressure and air density, forcing this air to the engine [38].

2.1 Fan Systems

There are three different fan systems: direct driven, hydraulic driven and electrical driven fans.

• Direct Fan Drive System

Direct driven fan systems use an old technology: the fan is either directly connected to the engine crank or driven by a belt mechanism. As there is dependency on the engine mechanical energy output, the speed of the fan is proportional to the speed of the engine. Excessive fan noise is a problem, especially during the vehicle’s acceleration through the gears. In addition, due to

Figure 2: Scheme of a turbocharger.Adapted from [39].

continuous fan rotation there is always energy consumption, even when it is not needed.

• Hydraulic Driven System

This type of system uses a fan with an electric motor and the coolant moves through the radiator by means of a hydraulic pump. Thus, this system is more complex because it requires the hydromotor, the hydraulic pump, control valves, oil, the coolant, connection hoses and hydraulic tanks. These components have high power density and high efficiency when compared to electric driven fans, for situations/vehicles that require high cooling rates.

• Electrical Fans

By definition, electrical fan defines the fan blade and the electrical motor. Since it is electrically driven, this system is easier to control. The fan is not driven by the engine ‘directly but by an alternator.

2.2 Radiator

The radiator is an aluminum mesh with a high number of fins all attached to the tubes that transport water and oil. There are two types of heat exchangers: unidirectional and cross flow heat exchangers, being the latter the most common in buses. In this case, the two fluid streams flow at right angles and so, fluid temperatures vary in both the direction of the flow and at right angles to that direction. Within the cross flow heat exchangers, the flow can be mixed or unmixed according to the temperature distribution from one row to another. The size of the heat exchanger matrix assumes primordial importance for the desired outcome of the cooling system to meet the specified heat transfer rate and pressure drop requirements. Bigger surface areas implies more drag and thus more cooling. The ideal radiator has to be wide, tall, thin and have a large frontal surface area, since the space constraint is a permanent issue. Regarding the fin density, high fin density means an increase in the pressure drop due to the reduction in the air flow, which can be a problem when the vehicle is stopped and when this restricts the air flow, being a problem for the case of the hydraulic fan. Lower fin density has the advantage of being easier to clean. In the case of hydraulic fans, the coolant flow rate to the radiator is also important:

the higher the flow rate, the higher the energy that can be removed from it. The temperature difference will be greater since the coolant will be moving at high temperatures as it is traveling through. The overall energy removed from the total system is less in the case of lower flow rates, even though the outlet temperature is lower. This is due to the fact that for higher flow rates, the temperature difference between the environment and the coolant is higher [41]. For air conditioning, there is another radiator, also called the air conditioner condenser, which also needs to be cooled. As long as the air conditioning is turned on, the fan keeps running, even when the engine is not at high temperatures.

Discharge

Impeller eye

Impeller

Impeller Volute

Figure 3: Scheme of a water pump. Adapted from [42].

2.3 Engine water pumps

In order to make the coolant flow from the engine to the radiator, a water pump is used. This process occurs by throttle heating, a mechanism by which the flow of a fluid is managed by obstruction or constriction. It controls the engine power by restriction of inlet gases. In an internal combustion engine a throttle is a valve that regulates the amount of air entering the engine, indirectly controlling the charge of air and fuel burned on each cycle. In a water pump, the majority of fluid is forced in a direction normal to the rotating axis of the water pump shaft. Thus, the rotor or impeller blades tend to be 2 dimensional and are more easily manufactured, unlike the mixed flow pumps where the blades take on a twist in the 3rd dimension [15]. As the coolant moves forwards, the diameter increases and so the area increases, leading to a consequent decrease of velocity and an increase of pressure.

At the outlet of the impeller there is a considerable velocity in the direction tangential of the outside circumference of the impeller that could be greater than the velocity required in the discharge section, which will lead to energy losses in the discharge section. To overcome this, the diameter of the casing increases along it, to provide an initial reduction in velocity, creating static pressure head as any addi- tional velocity. In this way, kinetic energy is converted in static pressure head. The diffuser helps the process as well, although it is limited by packaging constraints [60].

• Water pump design

When designing a water pump or a fan, the concept of system characteristic is used and is the sum of engine resistance, radiator resistance and thermostat resistance. The system characteristic is selected at a flow rate that corresponds to maximum engine power, being that the operating point. That corresponds to an operating condition that the water pump must match.

dP = KQ² (6)

In the equation 6, k is the system resistance in Ns².m⁸, dP the overall pressure drop in Nm⁻² and Q the system overall flow rate in m³s¹. In a water pump, the power is proportional to the engine speed to the power of 3 and the water flow rate is proportional to the engine speed. The water pump speed range is determined by package and speed limitations. It is driven by a belt from the crankshaft and has a drive ratio (crank to pump) between 1 and 1.3. The lower ratio is usually dictated by the package space available as this would render the maximum pulley diameter. The design of a water pump uses a tool called Cordier diagram. This diagram uses the specific speed and a dimensionless diameter related to

the outside diameter of the impeller, predicting its diameter for a given operating point. A common way of presenting machinery performances as function of the similarity is through correlation of the specific diameter, D0 (7) and the specific speed, Ns (8).

D0= DsQ^0,5

gdH^0,25 (7)

Ns= ωQ^0,5

gdH^0,75 (8)

The number of blades is also an important parameter in the design of a water pump. High number of blades implies frictional losses and blade blockage to flow, notwithstanding a better fluid conformity to blade direction. Normally five to ten blades is the most appropriate number. The eye diameter should minimize shock losses, that occur when the global direction of the coolant does not flow parallel to the drive shaft and in doing so can create an effect of collision of separate flow streams. Regarding the impeller inlet diameter, the higher the radial distance occupied by the blades, the more time the coolant has to gain the required velocity and the less violence is associated with the fluid’s passage through the impeller blades, leading to less cavitation problems and to a better control over the stress on the blades.

The inlet diameter is normally about 60% of the outlet diameter.

2.4 Charge air cooler

The charge air cooler is a heat exchanger that uses the compressed hot air from the compressor of the turbo-compressor and cools it, since it leaves the compressor at temperatures near 200 ℃with low density, this means that for the same volume there are less air particles and thus, the quantity of injected fuel will be less. So, decreasing the air temperature allows the introduction of more fuel that is used in a more efficient way since it has more space in the carburator. The temperature and pressure increase consequently the torque and the power of the engine. The charge air cooler works differently from the radiator since it only uses ambient air as a coolant. Despite this, there are also charge air coolers that use water as the coolant fluid. They are named air-to-water intercoolers and as they use water, they required more components such a pump and a water reservoir. For the time being, air-to-air charge air coolers are used in buses but some ideas about integrating an air-to-water with the radiator coolant are now on the table. The air-to-air type is cheaper but less effective and air-to-water has pressure losses [8],[4]. Regarding the design of the charge air cooler the criteria used are: the fin density, height and thickness. In a similar way to the radiator, the fin density can not be too high since it will decrease the velocity of the air and thus, lead to a bigger pressure drop. On the other hand, changing the height of the charge air cooler will not increase much the temperature difference between the ambient inlet air and the compressed air [44], [15].

2.5 Oil cooler

The oil cooler, used in the case of the hydraulic fan is positioned horizontally along the radiator’s lower edge or vertically along it. It is also an heat exchanger with oil as the coolant.

2.6 Fans shroud

The fan shroud is a plastic or metal funnel shaped piece on the back of the radiator (usually) that covers the fan(s) completely. It acts as a director for the air used to cool the radiator and to avoid air leakages between the fans and heat exchangers [56]. It is proved that excessive recirculation within the fan caused inefficient cooling but recent design improvements have tended to reduce recirculation and provided better cooling to underhood vehicle compartments.

2.7 Thermostats and other sensors

The purpose of the thermostat is

1. To help minimize the warm up time of the coolant;

2. To control the coolant temperature during normal engine running conditions once fully warm;

3. Allow the cooling pack to control coolant temperature when maximum cooling is required;

It does so by converting thermal energy into mechanical work. It is composed by a thermal motor containing wax element, a valve plate, a return spring and the body. By changing the state of the wax material from a solid into liquid, there is a conversion of thermal energy into mechanical work [46].

During warm phase the brass element is heated by the coolant and the heat is transmitted via conduction through the casing the and the wax. At a prescribed temperature the wax starts to melt and the resulting expansion pressurizes the rubber sleeve, forcing the piston outwards. The piston then reacts against the thermostat body to open the valve. During the warm up phase, the engine thermostat will be closed and the heater circuit in most cases will be open allowing coolant to flow through the engine and into the heater sub circuit but not through the radiator. When the thermostat opens and allows coolant to flow into radiator, the heater sub-circuit opens as well as allowing coolant to return back to the water pump inlet [60],[46]. Normally, the start-to-open temperature is 90 ℃[59]. A full piston travel of 9 millimeters is achieved at a temperature of 104 ℃, offering an active temperature range of 14 ℃. Working hand in hand with the thermostat, a relief valve not exposed to the coolant acts preventing that potential air pockets appear until the thermostat opens.

2.8 Header Tank and Recovery System

A typical cooling system needs a header tank and a recovery system to get a simple and convenient coolant filling point, allowing the expansion of the coolant without any losses. They have to be placed as high as necessary, since the coolant goes to the engine by hydrostatic pressure, due to the change in density, as the temperature decreases. The header tank (or expansion tank) has a pressure cap on the top. If the coolant boils and becomes vapor, which can cause serious damage since the heat transfer by conduction decreases. With the pressure cap, it is possible to change the temperature inside the header tank by changing the pressure inside [7],[60],[46]. As the coolant temperature rises, the coolant expands and pressure rises,above atmospheric pressure. In a recovery system, hot coolant flows out into the overflow container. As the engine cools, the coolant contracts and pressure in the radiator drops.

Atmospheric pressure in the overflow container then opens a second valve, a vacuum vent valve and overflow coolant flows back into the radiator. And that stops atmospheric pressure from collapsing the houses of the cooling system [7],[46].

3 Hydraulic Fans

When the cooling system uses a hydraulic fan, the engine’s control unit receives information on the engine’s temperatures from the coolant sensor. The hydraulic pump capacity is controlled by a pulse modulated signal (PWM) sent from the engine control unit to the solenoid valve on the hydraulic pump control valve, and the hydraulic pump’s oil pressure drives the wheel motor [15]. There is, in addition a rotational speed induction (or piston) sensor on the coolant fan, which reads the fan’s actual speed and returns this information to the engine control unit. When necessary, the output signal to the hydraulic pump is adjusted so that a correct rotational speed is maintained, in accordance with the engine thermostat and the remaining programmed parameters.

3.1 Coolant Temperature Sensor

The coolant temperature sensor measures the temperature of the coolant of an internal combustion engine. The information measured by the sensor is then sent to the engine’s control unit, being used after to adjust the fuel injection and time of ignition. The temperature sensor works through changes on resistance, that either increases or decreases according to a positive or negative temperature coefficient, respectively [7], [59].

3.2 Hydraulic pump

The hydraulic pump is mounted on the top of the engine or on the left side of the engine (rear). The pump’s pressure is controlled by the control valve (solenoid valve), via the PWM signal from the engine

Figure 4: Scheme of hydraulic valves

control unit. This releases requested amounts of hydraulic oil which increases or decreases the control plate angle. Thus, the pump piston has longer or shorter strokes, which increases or decreases the oil pressure [59].

3.3 Pump control plate

When the motor starts, the movable units inside the hydraulic pump housing start rotating.

1. When the control plate is vertical, the oil remains stationary in the cylinder barrel. This means that no oil is forced away and thus, no displacement.

2. The angle of the control plate means that the piston can move forwards and backwards in the cylinder barrel when the rotating unit turns and so, the pumping starts.

3. The amount of oil can vary, depending on the control plate’s angle. The larger the angle, the greater the displacement and higher the pump pressure.

3.4 Control valve and check valve

The control valve controls the upper valve. The longitudinal hole and the restriction on the check-valve make possible to build up the system’s pressure. This pressure acts the pre-tensioned spring. The restriction increases the system pressure in the control chamber. Depending on the electrical signal to the solenoid valve, a control pressure is obtained, which moves the main valve to its right.

3.5 Hydraulic fan motor

The hydraulic motor is a gear wheel type motor and is supplied in two different versions, depending on the bus specification. The oil pressure from the hydraulic pump is forced between the motor’s two gear wheels and starts the hydraulic motor. For most buses at Volvo Buses Corporation, idling speed can be 1120 rpm with a maximum rotational speed of 3000 rpm , that is reached at an engine speed of 1200 rpm. For other buses models, idling speed is equal to 750 rpm with a maximum rotational speed of 1950 rpm. Only when the engine reaches 1200 rpm the fan speed is maintained above 1800 rpm. A rotational speed induction sensor is located by the coolant fan and continuously reads the fan’s rotational speed, that is then sent to the engine’s control unit. When necessary, the output signal to the hydraulic pump is adjusted. The correct fan speed is therefore maintained with respect to the engine thermostat. There is also a hydraulic oil filter located inside the engine compartment and its purpose is to filter the oil on the return side.

4 Electrical Fans

An electric cooling fan system can reduce the fuel consumption and thus, the engine load compared to existing cooling systems that use hydraulic fans. Thus, in order to know how much energy savings it

is therefore important to know how is calculated the fan power.The transfer of mechanical energy is usually accomplished by a rotating shaft, and thus mechanical work is often referred to as shaft work; a fan receives shaft work (usually from an electric motor) and transfers it to the fluid as mechanical energy (less frictional losses). Laws of conservation must be taken into account when studying machines like fans and pumps.

• Conservation of mass

dm

dt = ˙min− ˙mout (9)

• Conservation of energy

dE

dt = d ˙Q − d ˙W+ ˙minein− ˙mouteout (10) where,

dE = change of energy d ˙Q= rate of heat added d ˙W = rate of work done

˙m = mass flow e= flow energy

Fans are a special case of fluid machines that consume power, like the compressors, but since their velocities are much lower it is assumed that the air flow is incompressible. Fans are used when the pressure differences are small enough that the density is considered constant . The work for the working gas is transformed on the pressure energy and the kinetic energy A fan set consists of a rotor followed by a stator and the energy equation for a the fan is shown in equation 11.

d ˙Q − d ˙W = ˙minein− ˙mouteout (11) d ˙Q − d ˙W = ˙min(∆KineticEnergy + ∆InternalEnergy + ∆P otentialEnergy) (12) Assuming potential energy neglected, the fan energy equation will be function of the kinetic and internal energy, related with flow velocity and temperature differences. There will be no heat exchange in the fan. The flow in fans is so slow that is always possible to regard it as incompressible. It is however not possible to say that the density is constant in the system equations, since it can vary with the operating point and with the location of the system. The density will vary with the temperature so, in the case of a bus cooling system, where two or more heat exchangers are present, the density change from ahead to after but the mass flow is the constant. If it is introduced pressure and assume the density constant through the fan unit, assuming air as an ideal gas,

h= u + p/ρ (13)

that,

−W = (pout

ρ + uout+v²_out

2 ) + (pin

ρ + uin+v²_in

2 ) = (pout

ρ −pin

ρ ) (14)

The Bernoulli equation is concerned with the conservation of kinetic, potential and flow energies of a fluid stream.

P ρ +V²

2 + gz = cte (15)

Therefore, the kinetic and potential energies of the fluid can be converted to flow energy, as a form of pressure. This can be seen by multiplying the Bernoulli equation by the density, ρ.

p +ρV²

2 + ρgz = cte (16)

where p is the static pressure used to evaluate fan performance, the second term the dynamic pressure and ρgz is the hidrostatic pressure, neglected in this case. This leads to the fan energy equation,

−W = ∆pf an

ρ +∆ploss

ρ (17)

The rotational energy from the engine is converted to electrical energy through an alternator to drive the electric motor(s). The motor again converts this electrical energy to rotational energy and then into flow energy. Some of this energy is useful but other output energy is wasted like the air swirl at the fan’s outlet. Concluding, the two types of useful energy in a fan are the static pressure (considered a form of energy) and the kinetic energy (due to the air particles movements). The kinetic energy is measured as the air flow rate. The fan performance is measured at atmospheric pressure and is a result of a combination of the two types of energy: kinetic energy and static pressure. The relative percentage of each type of energy will be dependent of the resistance of the system to be cooled by the fan [14]. An electrical fan system optimizes the operational efficiency due to the easiness of control the fan according to the engine load, regardless of the engine speed. Together with that, they are reliable and simple, even though they may not move as much air flow as a hydraulic fan. Hotter running engines have better thermal efficiency, which means that heat losses are reduced and intern more heat is used to make power. Electrical fans allow to safely increase the operating temperature of the coolant in the engine, which means less heat to rid of in the cooling system, which decreases the system capacity. In the cases where the hydraulic fans move more air than needed, electrical fans are beneficial. Other possible reasons for the less power required to reach the same cooling performance are:

1. Cooling performance (LAT, IMTD)

2. Oil cooler deleted (Power dissipated, static pressure) 3. nf an at vehicle (diesel) idling (stop-and-go test) 4. Heat rejection of the engine

5. Could be exhaust recirculation gas (EGR) mixed into the cold CAC-flow 6. Fan shroud design

7. Built-in-resistance 8. Derate strategy

9. Sandwich vs. Separated (rad and CAC) 10. TTT difference between the models

Roughly, can be said that the dissipated power is proportional do the mass flow power to 0,7, for higher air flows. For these air flows, the heat has to be dissipated and pressure drop will pay for this dissipated heat. This pressure drop is proportional to the mass flow to the power of 1,7. The fan can be modeled by its speed and the torque and the work done by the fan is the product between the fan speed and the torque.

Pdiss by the cooling module[W ] ∝ ˙m^0,7 (18)

∆Pf an∝ ˙m^1,7 (19)

The energy changes for fans are usually measured as pressure differences.

4.1 Radial, Axial fans and Diagonal fans

Fans can be radial or axial. For large volume flows and low pressure increase axial fans are preferred If the total pressure increase is very low, the rotor looks like a propeller. Axial fans are also used when the radial when the available radial space is restricted.

Radial Fans Radial fans (or blowers) are the most common ones used ones. The blades can be arranged straight ones in the radial direction, which is said to make the fan useful for gases contaminated with particles. They use a rotating impeller to move the air stream, increasing its velocity.The speed increases as it reaches the ends of the blades and is then converted to an increase in pressure. These fans can work under high temperatures and high pressurized conditions [23], [33].

CHAPTER 1. FANS

(a) Axial fan (b) Radial fan

Figure 1.1. Different types of fans

The fan in this thesis is a radial fan. The considered fan delivers the cooling airflow for an electric motor and is placed at the end of the motor and rotates with the same speed as the rotor. This is called an open self-ventilated motor.

The air flows axially into the inlet and through the channels in the motor and is deflected within the fan in order to leave the motor radial through the outlets.

In figure 1.2 the position of the fan is visualized at the back of the motor and the airflow is denoted by arrows.

Figure 1.2. Open self-ventilated electric motor 2

Figure 5: The effect of multiple fans on system pressure and flow rate. Adapted from [3].

Axial Fans Axial fans are normally used for cooling systems, since they allow large volume flows and low pressure increase. If the total pressure increase is very low, the rotor looks like a propeller. Axial fans are also used when the available radial space is restricted [28]. The blades in axial fans are mostly formed as wing profiles. To get a good efficiency, they should be skewed in the radial direction They work by moving an air stream along the axis of the fan. It can be compared to a propeller on an airplane:

the fan blades generate an aerodynamic lift that pressurizes the air [20], [23],[24]. They are inexpensive, compact and light which makes them the best choice for the cooling systems. The highest total efficiency is obtained with blades curved backward, even though they do not achieve an energy conversion as high as forward blades. However, this type of fan operates stably because the pressure difference provided by the fan drops if the flow rate goes up. If the opposite were true, an increased flow rate would cause increase fan power, which would be unstable [11]. This gives them the design advantage that makes them the best choice for the bus cooling systems.

Diagonal Fans Cooling fans for automobile industry have predominatly been axial fans since their low cost, thinness and ease of mounting. However, many tests show that due to the flow resistances in front and back of then fan are somehow strong (heat exchangers and front grille), the air flow direction tends to flow diagonally at the fan outlet side. An hybrid solution recently introduced in the market is called diagonal fans. These fans take an intermediate position between the axial and radial fans. Their configuration allows an air-flow similar to the axial fans whilst at the same time, achieving a higher static pressure, overcoming the problem of the counter pressure of the radial fans [45]. These fans have a conical rotor hub and they suck the air axially. This conical hub avoids vortex formation which reduces significantly the noise. The hub gas a small cross-section in the inlet area. In the outlet side, the diameter increases gradually, which provides an higher circumferential speed of the blade tips, meaning a higher centrifugal air acceleration[19]. Regarding the operating point of the diagonal fans, in comparison with axial fans, lies in a higher pressure range, which means that they can give more pressure with a significant higher air flow.

4.2 How to select the right fan

The first step is to know the total cooling requirements of the system. This can be translated in the needed air flow to dissipate heat. This air flow is calculated according to the power consumed by the system and the amount of air needed to remove heat from the system in order to do not increase its temperature.

2.2. NUMERICAL SIMULATIONS

Figure 2.3: Trace of static pressure through an engine bay.

small contribution from ram air (1)), so to overcome the pressure drop in the heat exchangers the fan is fully engaged and the major driver of airflow (5).

The red curve in Figure 2.3 represents a light load cruise condi- tion. Here, there is more access to ram air, and there is no significant need of cooling, hence the fan does not need to engage to any great extent.

The model used as a base in this thesis was proposed by Dav- enport [8] in 1974. Recently, work has been done on this model by Cowell [9].

This model has the form of Equation (2.1).

∆p

= ∆p

+ ∆p

+ 1

2 ρv

− 1

2 F ρv

(2.1) In this equation the notation in Table 2.1 apply.

Term Explanation

∆p

Fan Pressure Rise

∆p

Radiator or Cooling Package Pressure Drop

∆p

System Restriction

1

2

ρv

Fan Dynamic Head

1

2

F ρv

Ram Air Pressure, F is ram air effectiveness Table 2.1: Local nomenclature to Equation (2.1).

Figure 6: Change of static pressurer

4.2.1 The total cooling requirements

It must be known the heat as a temperature difference that must be transferred, the heat transfer power to offset the specified ∆T and the amount of air flow needed to remove the heat. The volume of air flow required can be thus calculated if one knows the internal heat dissipation and the total rise in temperature allowed.

Q= cP ∗ ˙m ∗ ∆T (20)

where,

∆ q = amount of heat transferred cP = specific heat of air

∆T = temperature rise

˙m = air mass flow

4.2.2 Static pressure

The total pressure of a system is the sum of the static pressure and the dynamic or velocity pressure.

The dynamic pressure is the pressure term of the Bernoulli equation associated with the velocity of the flow, and thus with the motion of the fluid.The static pressure is the pressure of the fluid if it were at rest. Thus it is independent of the air velocity but it is dependent of the air flow. Static pressure is also dependent on the blade profile, number of blades, pitch, hub space and aerodynamic characteristics of the fan impeller [17]. The force with which the air molecules move against the fan blades derives from static pressure. In this way, it is an indication of how much restriction a fan can overcome; higher static pressure means that a fan can push through a more dense radiator. A good way to understand this concept is to imagine using the fan to inflate a balloon; a fan with a higher static pressure would inflate the balloon to a larger size than one with a lower static pressure. The static pressure therefore can indicate how strong a fan is, and how good it is at overcoming resistance. [20]. The concept ”system resistance” is used when referring to the static pressure. The overall system resistance is the sum of static pressure losses, being also dependent of configuration of ducts and houses. The system resistance varies with the square volume of air flowing through the system.

4.2.3 Total System Resistance / System characteristic curve

To evaluate a specific fan with respect to its ability to transport a certain airflow, fan curves are used.

The pressure loss due to the resistance of the components of the cooling system varies with air flow and

21

CHAPTER 1. FANS

shut-off operating point

Q

Figure 1.5. Sketch of fan and system curve

0 0.5 1 1.5

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Q in m³/s

dP in Pa

Figure 1.6. System curve from ABB measurements

The system in our application is the set of channels and other conduits through the motor from the inflow from ‘free’ air to the outflow again to ‘free’ air. The system curve is determined by the flow resistances in the flow paths and is given in figure 1.6.

The fan curve can be measured if a prototype is available and is therefore pro- vided by the fan manufacturer. The fan curve can also be computed by using CFD software. This is done in this thesis.

The resulting intersection points are very useful to compare different fan designs 6

Figure 7: Sketch of fan and system curve. Adapted from [3]

is known as system resistance. It describes the amount of flow that will flow through the radiator and the charge air cooler; as more air is pushed through the radiator/CAC, more pressure is required. The system characteristic curve is given by:

Dp= KQn (21)

where K is the system characteristic constant, Q is the air flow, n a turbulence factor (1<n<2, whereas 1 is laminar and 2 turbulent flow.)

4.2.4 System Operating Point

A specific fan curve together with a specific system curve (or system impedance curve) of the cooled motor yield an operating point. This operating point represents the airflow that is delivered by the fan to the system. This means that in this point the fan is operating at the static pressure of that point and giving the respective flow, which is not the maximum flow rate. Thus, when selecting a fan is is not only important to look at the extreme values but to the system operating point[51].

4.2.5 Stall effect and instability regions

Stall on axial flow is a status of non uniform flow through the impeller of the fans that is translated in an unstable zone in the fan curves with a peak point as an indication of stall. During this condition, the flow is separated from the blade surface. Flow separation can be explain as the following: fan blades deflect the air, depending on its orientation relative to the flow direction. So if one change the orientation of the fan blade relative to the flow direction, it is possible to increase or decrease the amount that the air is deflected.That orientation is named angle of attack. If one increase gradually the angle of attack of the fan blade, it will increase the amount of air deflection. The angle of attack is responsible to the pressure differences between the upper and lower parts of the blades that allows the fan to lift and thus to move [12]. But if the angle of attack becomes too high, the air will no longer follow the blade surface in an uniform manner. The amount of deflection and the pressure difference being generated stops increasing and normally will fall off. This is called the stall point. In a fan, the blades are normally rotating at constant velocity. Therefore, to change the angle of attack, the system to which the fan is attached must be changed. Higher flow rates through the inlet increase the attack angle, and lower flow rates decrease it. Therefore, if a fan is operating in stall, it is because the air flow rate is too low for it. On a given system, this is caused by selecting a fan which is too large (making the air velocities too low in the fan) [22],[54],[58]. [14] [1] [2] [9] [61] [18]

4.2.6 Efficiency of electrical fans

The fan efficiency is the ratio between power transferred to the airflow and the power used by the fan shaft [32].

ηairf lowf anblade= Pout

Pin

(22)

STALLB REGION A

C

0 D

AIR FLOW

STATIC PRESSURE

RECOMMENDED SELECTION

RANGE Unstable region

STALL REGION

AIR FLOW

STATIC PRESSURE

A

B

C

D Stable region

Ƞ=100%

Rotational noise Non-rotational noise

EFFICIENCY

Figure 8: Stall: unstable zone in the fan curve

ηairf lowf anblade=∆pf an∗ _ρ^Q

f an

Pshaf t =∆pf an∗ _ρ^Q

f an

Pelec

∗ Pelec

Pshaf t (23)

Part V

Modeling and analyzing electrical fans

5 What is limiting electrical fans

5.1 Fan blade types

The blades in axial fans are mostly formed as wing profiles. A fan wheel must impart to the air stream an uniform velocity and pressure over its entire area. To get a good efficiency the blades must be skewed in the radial direction, which is said to make the fan useful when the air is contaminated with particles.

The fan is simple to manufacturer but will operate with low efficiency. The highest efficiency is obtained with blades curved backward. To get the impeller simpler to manufacture without loosing efficiency the backward swept blades are normally constructed as flat plates. The most advanced fan blades are made with a thickness distribution on the blade.

5.2 Fan Laws

If a fan curve has been measured for a specific speed, diameter and density, these laws can theoretically be used to calculate the fan curve for any other speed, diameter or density [26]. In order to better understand how does the fans work and compare between several configurations, the fan laws are used.

However, since these fans are electrical, the only two parameters that are allowed to scale for are the pressure and flow rate as a function of fan rotation rate. Efficiency and power consumption cannot be accurately scaled since they are a function of the electrical motor efficiency and fan blade efficiency[55].

System characteristic The static pressure is the difference between the absolute pressure in a point of air stream and the absolute pressure of ambient temperature. The total pressure in a point of a fan’s

airflow is the algebraic sum of the total pressure in that point and the velocity pressure. The velocity pressure is the pressure required to accelerate the air and is proportional to the kinetic energy. The fan total pressure is then the difference between the total pressure measured at the outlet and at the inlet of the fan. When choosing a fan for a cooling system, the fan static pressure is the parameter used and cannot be measured directly. It is the fan total pressure minus the dynamic pressure corresponding to the mean air velocity at the fan outlet [49]. The system resistance varies with the square of the air flow.

The affinity laws or fan laws establish that the volumetric air flow (AV) is proportional to the fan speed (N), the static pressure (∆p) is proportional to the square fan speed and the power (P) is proportional to the speed to power 3, if considered a constant impeller diameter (24). Since fan power consumption is highly sensitive to fan speed, significant energy savings are achieved if the fan can serve the system at a low speed. However, below about 40% of the motor load, fan efficiency begins to decline [50].

AV2

AV1

=N2

N1

∆p2

∆p1

= N₂² N₁²

P2

P1

=N₂³

N₁³ (24)

5.3 Influence of density

If the air temperature changes, then the density will be altered.Although the density change due to the flow is small. If a change in air density is considered, keeping the same fan model and the same air flow, the pressure and the fan power will be influenced by the density.

∆p2

∆p1

= ρ2 ρ1

P2

P1

=ρ2

ρ1 (25)

For the flow speed to be unchanged in a fan, the same air flow has to be considered. If the velocities are the same so the pressure increase over density is unchanged. When doing the combination of fans, it must be observed that it is the mass flow that is conserved and the pressure increase has to be matched.

For example, two fans in series do have the same mass flow but not necessarily the same volume flow, which is used in the fan diagram. It is also assumed that the pressure level in the heat exchangers will not be exactly the same for the several fans but it is assumed that such difference will not have any major impact in the density.

5.4 Impact of Fan Diameter

By increasing the diameter of the cooling fan, the same amount of air can be generated at a lower velocity. The area, A varies with the square of the diameter and so the velocity. The energy varies with the square of the velocity, v.

A ∝ D²; v ∝ D²; hp ∝ v² (26)

hp2= hp1

D1

D2

4 (27)

where,

hp1 - power draw of the existing fan hp2 - power draw of the desired fan D1 - diameter of the existing fan D2 - diameter of the desired fan

In the same way, flow rate and static pressure will be influenced by a change in diameter.

AV2

AV1

= D2

D1

3 ∆p2

∆p1

= D2

D1

2

P2

P1

= D2

D1

5

(28) A 10% larger fan will use less 32% hp to move the same amount of air. Thus, for instances, if one wants to reduce the fans diameter by 1/2, but still keeping the same air flow, following the fans laws:

Q ∝ N³ (29)

where Q is the air flow, N is the speed and D is diameter.

N1D³₁= N2D³₂ and D2= 0.5D1⇒ N2= 8N1 (30) The fans with half of the diameter will have to spin 8 times faster to provide the same air flow [10].