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A Thermal Bus for Vehicle Cooling Applications - Design and Analysis.

1. INTRODUCTION

Hybrid powertrains generate heat through the operation of the combustion engine, electric motors, generator, battery pack, and on-board electronics for propulsion. An important consideration is the cooling of these components to maintain the temperature within prescribed ranges. The emphasis on fuel consumption targets has necessitated a focus on power minimization including the cooling system in military vehicles [1, 2, 1, 4]. A variety of thermal management strategies exist as shown in Fig. 1. The most common cooling system design features an ethylene glycol liquid cycle radiator with fan, thermostat valve, pump, hoses, and engine block water jackets. Air cooled engines and components may be optional for lower heat loads. A novel design integrates both passive and active features that can be selected based on the operating conditions.

The monitoring and control of vehicle propulsion system temperatures can help ensure mission viability. Friction losses of engine parts vary as a function of lubricant and coolant temperatures with 90[degrees]C to 100[degrees]C the suggested oil temperature range [5]. The battery pack performance will decrease if its temperature is not properly maintained. Likewise, electrical components must be operated within their rated temperature range. In previous studies, cooling system architectures and their energy consumptions have been investigated for different operation conditions. Park and Jung [6] examined the thermal behaviors of three different cooling system designs to identify power consumption factors. Bayraktar [7] integrated computational fluid dynamics to study cooling system thermal behaviors. Tao and Wagner [3,8,9] adopted nonlinear control theory to regulate the electro-mechanical actuators operation schedules in engines. Wang et al, [1, 10] established mathematical models to optimize convection-based heat transfer by regulating actuator (e.g., fans, pump, and smart valve) operation. The radiator fan(s) consumes the greatest power within the engine cooling system [2].

The integration of energy-efficient passive heat rejection pathways in parallel with an active cooling for ground vehicles has not been fully investigated. An opportunity exists to innovate on the conventional cooling system to realize a flexible design that can accommodate increasing thermal loads and offer a "silent sentry" operational mode. The inclusion of high conductive materials/devices (e.g., heat pipes, composite fibers, alloys, etc.) may offer a potential solution for passive heat rejection within a smart architecture to move heat from the heat load(s) to ambient surroundings. In this study, the term "passive heat rejection pathways" refers to heat transfer modes which do not require vehicle supplied power. A starting point for a hybrid passive-active cooling system design will be the introduction of heat pipes. Loop heat pipes have been recognized as two-phase passive devices with high effective thermal conductivity which are capable of transferring heat at any orientation with respect to gravity [11]. Heat pipes are utilized in various thermal management applications to increase thermal conductivity and temperature distribution uniformity. For ground vehicles, heat pipes have been used to control component and compartment temperatures. Rao et al. [12] implemented an electric vehicle heat pipe based thermal management system to regulate the Li-ion battery temperature. El-Sharkawy [13] used heat pipes to control the catalytic converter temperature. Hendricks [14] introduced heat pipes to cool passenger cabins and reduce the A/C system operation schedule time. Lastly, Burban etal. [15] investigated the performance of pulsating heat pipes for vehicle cooling system applications in terms of number of turns and working fluids for various driving conditions.

The heat generated over the combustion process, propulsion and mechanical friction in ground vehicles must be managed effectively to ensure the system's durability and performance. An advanced automotive thermal management system is required to avoid exceeding the component's working temperature limits with minimum energy consumption in ground vehicles and enhance the engine performance. In this paper, the integration of passive heat rejection pathways in ground vehicle cooling systems is examined using a heat pipe based thermal bus with an attached cradle and heat exchanger with electric fan. The remainder of the paper is organized as follows. Section 2 introduces the thermal bus concept with cradle and heat exchanger. The corresponding mathematical model is presented in Section 3 to describe the dynamic behavior. Representative numerical results are discussed in Section 4 for a convoy escort driving cycle. The conclusion and Nomenclature List are contained in Section 5 and the Appendix, respectively.

2. HYBRID COOLING SYSTEM STRATEGY

Hybrid ground vehicles are typically composed of an internal combustion engine with electrical motor, electro-mechanical components, and accompanying battery packs in either a parallel or series configuration. The powertrain components generate a significant amount of heat that must be dissipated through the cooling system. In some instances, the heat rejection may be modest which reflects either a sentry type operating mode or low speed high efficiency electrical motor propulsion. For this case, a passive thermal management system may be designed to handle the cooling needs. The proposed advanced cooling system structure features a passive cooling heat rejection pathway associated with a smart active cooling system structure which operates based on the heat rejection needs. The recognition that a passive cooling approach for large prolonged thermal loads, especially internal combustion engines, will be insufficient leads to a hybrid design that also features a conventional radiator-pump configuration.

The individual heat loads may be interfaced to a thermal bus through an optimized surface area called a "cradle". The cradle must be designed based on each individual heat load heat generation rate, operation conditions, and shape. Components with low convective heat transfer to surroundings may benefit by large cradle coverage. A cradle with high thermal conductivity and small thermal expansion provides the needed thermal connection between the heat sources and thermal bus. The external surface of the cradle will be encased in a low conductivity insulating material to route energy in the desired direction.

The thermal bus transports heat from the cradle to the radiator with attached fan(s). The thermal bus is defined as any devices, including passive or active heat transfer pathways, used to transfer heat from a given entity. For instance, devices using liquid based cooling to passive advanced materials with high thermal conductivity. The proposed thermal bus concept features a computer-controlled liquid cooling system which give the system capabilities to handle high heat removal needs if the temperatures of the heat load components become excessive. Figure 2 shows a concept of a hybrid cooling system which benefits from passive cooling system in parallel with active cooling strategy. High conductive materials such as composite fibers, alloys, phase change materials as well as high thermal conductive passive devices like heat pipes will be implemented into the passive cooling strategy. Heat will be transferred between two points with temperature gradient. Studying high thermal conductive materials provides the foundation of understanding their thermal performance. Similarly, heat pipe structures are highly efficient systems which can be integrated in a wide variety of cooling applications which essentially extends their functional possibilities in practical applications.

The integration of a high efficiency heat exchanger with an optional electrical fan(s) will increase the efficiency of the cooling system. A control strategy will be needed to operate the heat exchanger fan(s) through the monitoring of system temperatures and minimize power consumption while meeting the thermal demands for each component per various operating scenarios. Overall, the proposed cooling system may benefit from a lower weight system structure, enhanced flexibility and reliability, silent mode operation, high effective thermal conductivity, and smaller external power consumption.

3. MATHEMATICAL MODEL

Several mathematical models have been developed for the thermal bus system from the heat load, to the cradle to the heat exchanger. These include several models for pulsating U-shaped heat pipes (PHP) to study the impacts of various design parameters such as initial conditions, diameter, charge ratio, temperature difference and working fluid on the oscillatory behavior and performance of heat pipes [16, 17]. Heat pipes can be included as both parts of the cradle and/or the thermal bus. Results have shown the heat pipe diameter and temperature difference are effective factors on heat pipe heat transfer rates. It's been proven that heat is mainly transferred due to the exchange of sensible heat compared with latent heat [16]. Ma et al. [18] studied the effect of nano-fluid on oscillating heat pipe heat transfer rate. They proved that using nano-fluid as working fluid results in a significant temperature difference reduction between the evaporator and condenser sections in oscillating heat pipes. Yang et al. [19] have examined heat pipes in terms of light weight and performance and highlighted some limitations to the application of light weight material in heat pipes.

A reduced order passive cooling system containing a heat load, cradle, thermal bus, and a finned heat exchanger is numerically formulated and analyzed to describe the thermal behavior over the operation cycle. Figure 3a shows the flow of thermal energy and Fig. 3b displays the corresponding nodal network. The heat generation rate of the heat load will be set based on each heat load individually. The e-motor generates a significant amount of heat in comparison with the other heat loads in the ground vehicle. Therefore, a passive cooling system with the associated e-motor with respect to an actual driving cycle is investigated in this study.

3.1. Cradle Structure

The heat load cradle is used to efficiently transfer heat from the thermal load to the thermal bus (in this case the evaporation section of the pulsating heat pipe). Metals with high thermal conductivities are widely used as the media to transfer heat from the thermal load to the evaporation section of the heat pipe. Heat pipe embedded copper bases are widely used to transfer heat from microelectronics. A heat pipe based cradle can operate to dissipate heat from the heat load to the thermal bus. The configuration of the cradle is dependent on the structure of the thermal load. The cradle is assumed to be ideal in the current simulation so that the cradle can be considered as a simple thermal resistance so that:

[mathematical expression not reproducible] (1)

where [R.sub.cra] is the thermal resistance of the cradle, [x.sub.cra] is the thickness of the cradle, [A.sub.cra] is the surface area vertical to the heat flow direction, and [k.sub.cra] is the thermal conductivity of the cradle. The entire system temperature of the cradle selected as the output such that:

[mathematical expression not reproducible] (2)

where [T.sub.BI] is the thermal bus input temperature.

3.2. Thermal Bus

The thermal bus is composed of multiple U-shaped pulsating heat pipes which is in thermal contact with the heat load. The pulsating heat pipes are partially filled with working fluid. The working fluid is specified based upon the rated operation temperate range of the intended heat load, in this case an e-motor. Once the heat load generates heat, the vapor pressure quickly increases within the evaporator section. The pressure difference between the vapor plug and liquid plug keeps the vapor in one end and moves the liquid toward the other end of the pipe. The liquid section condenser releases the latent heat toward the ambient or a heat exchanger. The vapor is always exposed to the liquid at the split line where vapor continuously condenses or liquid vaporizes due to the temperature difference between the evaporator and condenser sections. The heat pipe condenser section is always exposed to ambient surrounding or attached to an external heat sink. In the developed numerical model, the heat pipe based thermal bus is attached to a heat exchanger. Figure 4 shows a schematic diagram of a pulsating heat pipe where [L.sub.h] is the evaporator length and [L.sub.c] is the condenser length. Since it is partially filled there are both liquid and vapor in the tube. The straight tube shown in Fig. 4b illustrates the condenser, evaporator, and total length of the pulsating heat pipe model.

For practical purposes, the pulsating heat pipe model [12] is applied hereinafter for each single heat pipe. A summary of the model is presented below and further details can be found in the citation. For present purposes a heat pipe based model for only the thermal bus is developed (while future work could incorporate heat pipes into the cradle and/or heat exchanger).

Establishing the mathematical model of the U-shaped pulsating heat pipe needs six fundamental assumptions to simplify the problem:

A.1: Vapors follow the ideal gas law.

A.2: Liquid is incompressible.

A.3: Mass transfer between the liquid and vapor is small and does not affect the liquid's total mass.

A.4: Evaporation and condensation heat transfer coefficients are constants.

A.5: Evaporation only happens when liquid is in the evaporator section and condensation only happens when vapor is in the condenser section.

A.6: The heat pipe is ideally insulated.

Once the heat source generates heat, the working fluid is accumulated in the liquid condenser section and vapor occupies the volume to the evaporator section as shown in Fig. 4a. The liquid slug can be assumed as a particle in tube since the liquid is incompressible and the mass transfer between the liquid and vapor sections is assumed negligible. The vapor apply force toward the liquid section from both vapor sides (shown by yellow arrays in Fig. 4b) due to the pressure difference created due to their temperature difference between the condenser and evaporator sections. Other forces that influence the fluid motion include shear stress that acts on the shell and gravity if the tube is oriented in a vertical direction. The momentum equation of the liquid is expressed based on Newton second law:

[mathematical expression not reproducible] (3)

where [[rho].sub.1] denotes the density of the liquid, [L.sub.p] is the length of the liquid, and [p.sub.v1] as well s [p.sub.v2] represent the pressure of the left hand and right hand sides of the vapor, respectively. The term [DELTA][p.sub.b] corresponds to the pressure loss at the bend. The cross section area of the heat pipe is denoted by A while d is the tube diameter.

The shear stress and the pressure loss due to the bend in the pipe are expressed as follows:

[mathematical expression not reproducible] (4)

[mathematical expression not reproducible] (5)

where [xi] is the pressure loss coefficient and [v.sub.e] denotes the liquid viscosity.

Eg. (3) can be rearranged as Eq. (6):

[mathematical expression not reproducible] (6)

Applying the first law of thermodynamics to the energy equations of the vapor plugs, the following equations are achieved:

[mathematical expression not reproducible] (7)

[mathematical expression not reproducible] (8)

Solving partial derivative of Eqs. (7) and (8) with respect to Eq. (9) and simplifying the results, Eqs. (7) and (8) can be rearranged as follows:

[C.sub.p] - [c.sub.v] = R (9)

[mathematical expression not reproducible] (10)

[mathematical expression not reproducible] (11)

The equations of vapors are simplified with respect to ideal gas law as:

[p.sub.v1]A([L.sub.h] + x) = [m.sub.v1]R[T.sub.v1] (12)

[p.sub.v2]A([L.sub.h]-x) = [m.sub.v2]R[T.sub.v2] (13)

Differentiating Eqs. (12) and (13) leads to:

[mathematical expression not reproducible] (14)

[mathematical expression not reproducible] (15)

Substituting Eq. (10) into Eq. (14). and Eq. (11) into Eq. (15):

[mathematical expression not reproducible] (16)

[mathematical expression not reproducible] (17)

Defining [gamma] = [c.sub.p]/[c.sub.v] and integrating Eqs. (16) and (17). the mass of vapors can be expressed as:

[m.sub.v1] = C[[p.sub.v1].sup.1/[gamma]](x + [L.sub.h]) (18)

[m.sub.v2] = C[[p.sub.v2].sup.1/[gamma]]([L.sub.h]-x) (19)

where C is an integration constant. The integration constant is constant in the tube since the tube is assumed to be symmetric. The vapor temperatures are acquired by substituting Eq. (18) into Eq. (12). and Eq. (19) into Eq. (13):

[mathematical expression not reproducible] (20)

[mathematical expression not reproducible] (21)

The equations of mass change rate between the liquid and vapor slugs are expressed as follows:

[mathematical expression not reproducible] (22)

[mathematical expression not reproducible] (23)

where [h.sub.fg] is the latent heat coefficient. The final equations for the latent heat can be obtained by:

[mathematical expression not reproducible] (24)

[mathematical expression not reproducible] (25)

The total latent heat in and out of the heat pipe can be calculated by adding the latent heat in vapor 1 and vapor 2 together:

[Q.sub.v_in] = [Q.sub.v1] + [Q.sub.v2] (When [Q.sub.v1] > 0, [Q.sub.v2] > 0) (26)

[Q.sub.v_out] =-[Q.sub.v1] - [Q.sub.v2] (When [Q.sub.v1]<0, [Q.sub.v2] < 0) (27)

It is essential to determine the temperature field of the liquid slug in the heat pipe to acquire the sensible heat. Since the liquid temperature varies with both time and location a small unit liquid slug was analyzed. It is assumed that the temperature of liquid equals the vapor temperature at their interface. Figure 5 shows the heat transferred considering a small unit length of the liquid slug.

The total heat in this unit element can be expressed as [mathematical expression not reproducible], heat transferred from the left end to the right end can be expressed as [mathematical expression not reproducible], heat transferred between liquid and the outside surroundings which could be either the heat exchanger or the cradle can be expressed as [h.sub.lse][pi]ddx([T.sub.1] - [T.sub.w]) where [T.sub.w] is the wall temperature. It could be either the thermal bus input temperature [T.sub.BI] in the evaporator section or the heat exchanger temperature in condenser section. As a result, the temperature of the liquid can be written as:

[mathematical expression not reproducible] (28)

where [[rho].sub.1] and [c.sub.pl] are the liquid's density and heat capacity, respectively. And, [lambda] represents the thermal conductivity.

The sensible heat transfer can be expressed by Eqs. (29) and (30) once the liquid temperature distribution is obtained:

[mathematical expression not reproducible] (29)

[mathematical expression not reproducible] (30)

After the sensible heat is acquired, the total heat transferred by this heat pipe based thermal bus can be calculated by adding the sensible heat and the latent heat together:

[[Q.sub.total].sup.-] [Q.sub.v_out] + [Q.sub.sen_out] (31)

The heat removal by the thermal bus then can be expressed by multiplying by the number of heat pipes, n:

[Q.sub.removal]= [Q.sub.total] x n (32)

3.3. Heat Exchanger and Fan Assembly

Implementing a heat exchanger into the cooling structure will increase the system capabilities in dissipating heat to ambient surrounding. Shah [20] explored the recent improvements in heat exchanger and radiator designs. An ideal heat exchanger should be able to dissipate the heat through natural convection in normal conditions while an active cooling cycle is always available to start operating once temperatures become excessive. The advanced cooling system is essentially featured with a mechanism which operates the active mode in harsh conditions. In this manner, the passive heat exchanger always cools the system with low energy consumption while the active mode can handle high heat rejection needs once heat rejection requirements exceed passive heat rejection mode capacity. The proposed advanced heat exchanger benefits of fin structure which enhances heat rejection capacity. Fin structures can greatly promote the heat transfer by enlarging the heat transfer surface area. The governing equations for the heat exchanger are set up as follows once the air velocity due to the fan operation, angel of attack and the speed of the vehicle are determined:

[mathematical expression not reproducible] (33)

Here, [q.sub.f] corresponds to the heat rejected due to the radiator fan operation, [m.sub.f] denotes radiator fan air mass flow rate, [T.sub.BO] and [T.sub.m] are radiator and ambient temperatures, respectively, and [c.sub.pa] corresponds to heat capacity of the air. The air ram effect is:

[q.sub.ram] =f([v.sub.speed], [v.sub.air], [[alpha].sub.wind]) (34)

where [q.sub.ram] denotes the heat rejected due to ram effect, [v.sub.speed]. represents the vehicle speed, [v.sub.air] is the wind velocity, and [[alpha].sub.wind] corresponds to the attack angel of the wind with respect to the position of the radiator. The radiator temperature is calculated as:

[mathematical expression not reproducible] (35)

where [mathematical expression not reproducible] is the coolant mass flow rate, and [c.sub.r] and [c.sub.pc] denote the heat capacity of the radiator and the coolant, respectively, and [T.sub.BO] represents the radiator temperature.

In the thermal bus output section an air heat exchanger with fin structures is applied to enhance heat rejection. And a fan can be used to blow air to increase heat transfer. Fin structures can greatly promote heat transfer by enlarging the heat transfer surface area. When the fin dimensions are determined the forced convection coefficient can be approximately expressed by:

[h.sub.f] = 10.45 - [v.sub.air] + 10 x [square root of ([V.sub.air])] (36)

where [v.sub.air] is the air velocity. Fin efficiency theory is adopted to calculate the fin effective area:

[mathematical expression not reproducible] (37)

in which [A.sub.f] is the area for one fin [A.sub.t] is the total fin area [[eta].sub.f] is the fin efficiency [10]. The thermal resistance of the heat exchanger then can be acquired based on Eqs. (26) and (21

[mathematical expression not reproducible] (38)

The heat rejection then can be calculated by:

[mathematical expression not reproducible] (39)

The above set of governing equations thereby describe the overall system performance from heat load to energy transfer to ambient.

4. Case Study--Electric Motor with Passive Thermal Management System

A numerical simulation study was conducted to evaluate the thermal behavior of an electric motor with integrated passive cooling system. The complete cooling system has been modeled and simulated including the heat load, cradle, passive thermal bus, and a finned air cooled heat exchanger with electric fan. This case study will examine the system performance for representative driving scenarios. The convoy escort, shown in Fig. 6, displays the vehicle speed and electric motor heat generation as functions of time. This simulated driving profile corresponded to a group of military vehicles traveling at moderate speed with some variations in power train demand. The heat generation of electric motors rate does not typically exceed 3 kW over normal driving conditions in hybrid vehicles for drive cycles analyzed in this study, but sudden accelerations may influence the heat generation rate significantly.

Figure 7 displays the structure of the simulated passive cooling model. The heat is initially channeled to the thermal bus through a designed aluminum cradle surrounding the electric motor. A wide variety of high thermal conductive materials and passive devices were considered. A heat pipe based thermal bus is the preferred initial solution for the thermal bus studies due to the high heat flux transport capability and structure flexibility. The heat pipe based thermal bus is driven by the temperature gradient. As long as the temperature difference exists across the thermal bus, the heat is continuously transferred from the heat load to the heat exchanger with attached electric fan.

A reduced order passive cooling system has been numerically modeled per Section 3 to transfer motor generated heat from the cradle to the heat exchanger. The model parameters are summarized in Table 1.

The convoy escort driving cycle (refer to Fig. 6b) was supplied to simulate the temperature of the electric motor. The corresponded electric motor temperature is shown in Fig. 8. It is interesting to examine the event at t=2000 (s) which reflects the vehicle acceleration. It causes a sudden growth in the generated heat and consequently the temperature of the heat load rises. The cradle temperature, as expected, follows the electric motor temperature variation trend with small temperature difference. Then, the heat is moved to the thermal bus which transfers the heat to the heat exchanger. Finally, the heat exchanger discharges the heat to the ambient surrounding set on 25 [degrees]C. Figure 8 contains the data of the heat exchanger temperature. The peak in heat exchanger temperature at t=2000 (s) occurs as the consequence of the vehicle acceleration. The operation temperature of the e-motor is generally maintained lower than 90 [degrees]C over normal driving conditions. However, integration of an active cooling system in parallel with the passive cooling strategy will improve the capability of the cooling system in handling the higher heat rejection needs over aggressive driving conditions or sudden accelerations or decelerations.

The performance of the heat pipe based thermal bus is shown in Fig. 9. It shows how the liquid slug is fluctuating due to the heat transfer between the vapor and liquid slugs in the pulsating heat pipe. The heat transfer between the liquid and the vapor slugs is a continuous process as long as there is temperature gradient across the heat pipe based thermal bus. Figure 9 also shows vapor temperature variations, vapors pressure variations and the vapors mass variations as functions of time. The vapor mass variations over the evaporation and condensation process are infinitesimal which confirms the assumption made for constant liquid length.

The heat entering the cooling system and the heat exiting the heat exchanger with respect to convoy escort driving cycle as plotted in Fig. 10.

5. CONCLUSION

The cooling of the powertrain components and electronics in ground vehicle remains an open challenge. The integration of a passive cooling strategy with active features offers a potential solution to reduce the energy consumption in military ground vehicles. This study investigated the passive heat rejection using a heat pipe based thermal bus with attached cradle and heat changer with electric fan. Mathematical U-shaped pulsating heat pipe model was used to numerically describe the thermal behavior of heat pipe based thermal bus. The case study focused on the convoy escort driving cycle for hybrid vehicles to investigate the system performance based on e-motor loadings. The simulation results demonstrate that moderate thermal load can be transferred to the ambient for heat rejection. This approach avoids the operating of a fluid cooling system and radiator fan cycled off if ram air speed is sufficient across the heat exchangers. Simulation results indicate that the heat dissipation rate of the thermal bus is significantly influenced by heat pipe length, diameter and the temperature difference between the heat load and the ambient surrounding. The next step will be experimental validation of the numerical findings through laboratory tests.

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Shervin Shoai Naini, Junkui (Allen) Huang, Richard Miller, and John R. Wagner

Clemson University

Denise Rizzo and Scott Shurin

US Army TARDEC

Katherine Sebeck

TARDEC

CONTACT

Corresponding author:

J. Wagner

Department of Mechanical Engineering, 212 Fluor Daniel Building, Clemson University, Clemson, SC, 29634, USA

jwagner@clemson.edu

ACKNOWLEDGMENTS

The authors wish to acknowledge the financial and technical support of the U.S. Army Tank Automotive Research Development and Engineering Center (TARDEC), and the Automotive Research Center (ARC) at the University of Michigan and Clemson University.

APPENDIX: NOMENCLATURE LIST

A - Heat pipe cross section area, [m.sup.2]

[A.sub.cra] - Cradle surface area, [m.sup.2]

[A.sub.eff] - Effective fin area, [m.sup.2]

[A.sub.t] - Total fin area, [m.sup.2]

C - Integration constant

[c.sub.p] - Vapor heat capacity at constant pressure, J/kg.K

[c.sub.Pa] - Air heat capacity, J/kg.K

[c.sub.Pc] - Coolant heat capacity, J/kg.K

[c.sub.pl], - Liquid heat capacity, J/kg.K

[c.sub.r] - Radiator heat capacity, J/kg.K

[c.sub.v] - Vapor heat capacity at constant volume, J/kg.K

d - Inner diameter, m

g - Gravity factor, [m/s.sup.2]

[h.sub.c] - Heat transfer coefficient at wall, W/([m.sup.2].K)

[h.sub.e] - Heat transfer coefficient, W/([m.sup.2].K)

[h.sub.f] - Convection coefficient, W/[m.sup.2]

[h.sub.fg] - Latent heat, J/kg

[h.sub.lse] - Heat transfer coefficient in liquid, W/[m.sup.2]

[K.sub.cra] - Cradle thermal conductivity, W/m.K

[L.sub.c] - Cold section length, m

[L.sub.h] - Hot section length, m

[L.sub.p] - Liquid slug length, m

n - Number of heat pipes

N - Number of fins

[m.sub.v1] - Vapor 1 mass, kg

[d[m.sub.c].bar] Vapor 2 mass, kg

[d[m.sub.f].bar] - Coolant mass flow rate kg/s

dt - air mass flow rate kg/s

[DELTA][p.sub.b] - Pressure loss at bend, Pa

[p.sub.v0] - Initial pressure of vapors, Pa

[p.sub.v1] - Vapor 1 pressure, Pa

[p.sub.v2] - Vapor 2 pressure, Pa

[q.sub.f] - Heat rejected due to fan operation, W

[Q.sub.Load] - Heat load heat generation rate, W

[q.sub.ram] - Heat rejected due to air ram effect, W

[Q.sub.Removal] - Thermal bus heat removal, W

[Q.sub.Rej] - Heat exchanger heat rejection, W

[Q.sub.sen_in] - Sensible heat transferred in liquid, W

[Q.sub.sen_out] - Sensible heat transferred out of liquid, W

[Q.sub.Total] - Total heat transferred by thermal bus, W

[Q.sub.v_in] - Total latent heat input, W

[Q.sub.v_out] - Total latent heat output, W

[Q.sub.v1] - Latent heat from vapor 1, W

[Q.sub.v2] - Latent heat from vapor 2, W

R - Gas constant, J/kg. K

[R.sub.cra] - Thermal resistance of cradle, K/W

[R.sub.exc] - Thermal resistance of heat exchanger, K/W

[T.sub.BI] - Evaporator temperature, K

[T.sub.BO] - Condenser temperature, K

[T.sub.L] - Temperature of liquid, K

[T.sub.Load] - Thermal load temperature, K

[T.sub.v0] - Initial temperature of vapors, K

[T.sub.v0] - Temperature of vapor 1, K

[T.sub.y0] - Temperature of vapor 2, K

[T.sub.w] - Wall temperature, K

[T.sub.[infinity]] - Ambient temperature, K

v - Wind velocity, m/s

[v.sub.e] - Liquid viscosity, [m.sup.2]/s

[v.sub.speed] - Vehicle speed, m/s

[v.sub.air] - Wind velocity, m/s

X - Displacement of liquid, m

[X.sub.cra] - Thickness of cradle, m

[[alpha].sub.wind] - Angel of attack

[[rho].sub.1] - Working liquid density, kg/[m.sup.3]

[[pi].sub.1] - Shear stress, N/[m.sup.2]

[gamma] - Ratio of [c.sub.p]/ [c.sub.v]

[lambda] - Thermal conductivity, W/m.K

[xi] - Pressure loss coefficient

doi: 10.4271/2017-01-0266.
Table 1. Summary of model parameters with values.

Symbol                Value            Unit

[A.sub.cra]              0.065         [m.sup.2]
[A.sub.eff]              0.3549        [m.sub.2]
[C.sub.p]             1930              J/kg.K
[C.sub.pl]            4182              J/kg.K
[C.sub.v]             1460              J/kg.K
d                        0.005             m
g                        9.8          m/[s.sub.2]
[h.sub.c]              200          W/([m.sub.2].K)
[h.sub.e]              200          W/([m.sub.2].K)
[h.sub.fg]         2257000               J/kg
[L.sub.c]                0.3               m
[L.sub.h]                0.3               m
[L.sub.p]                0.6               m
[p.sub.v0]           31164                Pa
R                      462              J/kg.K
[DELTA]t               [10.sup.-4]         s
[T.sub.v0]             303                 K
[T.sub.[infinity]      298                 K
[V.sub.air]              2                m/s
[V.sub.e]                0.801e-6     [m.sup.2]/s
[X.sub.cra]              0.0254            m
[X.sub.0]                0.05              m
[[rho].sub.1]         1000           kg/[m.sup.3]
[lambda]                 0.61            W/m.K
[xi]                     0.31              -
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Author:Naini, Shervin Shoai; Huang, Junkui (Allen); Miller, Richard; Wagner, John R.; Rizzo, Denise; Shurin
Publication:SAE International Journal of Commercial Vehicles
Article Type:Technical report
Date:May 1, 2017
Words:5836
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