Eduardo Sebastián
email: sebastianme@inta.es

Carlos Armiens

Javier Gómez-Elvira

Pyrometer model based on sensor physical structure and thermal operation

Keywords: IR temperature sensor, Sensor thermal model, Sensor calibration, Spacecraft instrumentation

This paper proposes a new simplified thermal model for pyrometers, which takes into account both their internal and external physical structure and operation. The model is experimentally tested on the REMS GTS, an instrument for measuring ground temperature, which is part of the payload of the NASA MSL mission to Mars. The proposed model is based on an energy balance equation that represents the heat fluxes exchanged between sensor elements through radiation, conduction and convection. Despite being mathematically more complex than the more commonly used model, the proposed model makes it possible to design a methodology to compensate the effects of sensor spatial thermal gradients. The paper includes a practical methodology for identifying model constants, which is part of the GTS instrument calibration plan and uses a differential approach to avoid setup errors. Experimental results of the model identification methodology and a target temperature measurement performance after identification has been made are reported. Results demonstrate the good behaviour of the model, with errors below 0.15ºC in target temperature estimates.

Introduction

In the study and design of IR sensors, and more specifically of thermopiles, physical models of their internal structure are used [START_REF] Escriba | Complete analytical modelling and analysis of micro-machined thermoelectric uncooled IR sensors[END_REF][3] [START_REF] Grafa | Seebeck's affect of micro-machined thermopiles on infrared detection[END_REF]. Amongst other parameters, these models take into account: the thermal conductivities of the construction materials, convection and radiation heat This study is unlike the work usually carried out with IR sensors as pyrometer, which uses sensor models that do not take into account the internal structure of the thermopile [START_REF] Muller | Large highly sensitive thin-film thermopiles as radiometric detector standard[END_REF] [START_REF] Grafa | Seebeck's affect of micro-machined thermopiles on infrared detection[END_REF]. The usual way of dealing with these sensors is through an equation that associates the electrical output variable of the transducer with the difference in radiated energy between the transducer and the target using a gain, the value of which depends on the temperature of the transducer [START_REF] Escriba | Complete analytical modelling and analysis of micro-machined thermoelectric uncooled IR sensors[END_REF].

The main advantage of this simple model is that it is easy to implement in practical applications, does not require high computational capabilities, and in some cases a simple analogue amplifier is enough to obtain a representation of the target temperature [6]. Other authors [START_REF] Pezzotti | Low radiation pyrometer for measuring forehead skin temperature[END_REF] propose a direct polynomial interpolation between the transducer output voltage and temperature with the target temperature, obtaining high accuracy. The main drawback with all these models is that they do not include a representation of the physical structure and operation of the sensor, as there is no direct relation between any physical property and the model parameters.

Taking into account the structure of the internal IR sensor in the model sensor may help us to understand its behaviour after its change or degradation, or the appearance of temperature gradients in its structure, being the capability of establishing calibration or compensation algorithms for those parameters that are directly related to sensor physical behaviour. For instance, in [START_REF] Foote | Temperature stabilization requirements for unchopped thermal detectors[END_REF] the author proposes an internal thermal equilibrium equation, for different kinds of unchopped thermal detectors, to model its sensibility to changes in instrument temperature.

The authors of [START_REF] Liess | Stabilization of the output signal of thermopile sensors in the thermal environment of automotive applications[END_REF] go beyond that in an attempt to establish a methodology, also based on a simplified internal model of a thermopile, which avoids errors that stem from sensor temperature instabilities or temporal gradients. In [START_REF] Boidens | International patent WO 2008/139321 A1, Infrared Radiometer[END_REF] the author proposes an IR sensor concept, based on its internal operation, which accounts for the sensor's behaviour under the existence of spatial temperature gradients on its can. Finally, in [START_REF] Ploteau | Conception of thermoelectric flux meters for infrared radiation measurements in industrial furnaces[END_REF] the authors discuss a thermal model for a thermo electric flux meter, consisting of a thermoelectric device and based on its physical construction and parameters.

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The main contribution of this article is the proposal of a new simplified analytical thermal model for pyrometers based on the sensor's physical structure and operation. The proposed model accounts for the heat fluxes exchanged between the sensor's transducer and the rest of its elements through radiation, conduction and convection. It also includes an estimator to compensate for the appearance of the thermopile's spatial thermal gradients, but contrary to the generic solution given in [START_REF] Boidens | International patent WO 2008/139321 A1, Infrared Radiometer[END_REF], this estimator makes use of the temperature evolution of an external temperature sensor. With the model a differential methodology to calibrate its constants can be established. The experimental data corroborate the ability of the proposed model to represent sensor behaviour, identifying model constants and showing its ability to measure the temperature of a target surface.

Brief description of REMS GTS

This study was originally motivated by the application of a pyrometer in space, the Ground Temperature Sensor (GTS) of the Rover Environmental Monitoring Station (REMS) [START_REF] Gomez-Elvira | REMS, an instrument for Mars Science laboratory Rover[END_REF], which is part of the NASA Mars Science Laboratory (MSL) mission to Mars [9]. This pyrometer is used to measure kinematic ground temperature, integrating the radiation of the Martian surface in three different infrared wavelength channels. The GTS has a total size of 40x28x19mm and a weight bellow 20g, see Fig. 1. It is formed by three TS-100 thermopiles supplied by the company IPHT Jena [10], encapsulated inside a TO-5 and facing the ground with no optical system apart from the thermopile filter. The thermopiles have an internal Resistance Temperature Detector (RTD) to measure the temperature of the base of their can T cb , which acts as the cold junction reference temperature of the thermocouples, and a non corrosive, insulating and transparent filling atmosphere. The thermopiles are situated inside a metal piece used as a thermal mass to minimize the temporal and spatial drift in their temperature [START_REF] Liess | Stabilization of the output signal of thermopile sensors in the thermal environment of automotive applications[END_REF].

In remote or hostile applications, recalibration and optic cleaning systems are key features of any pyrometer. In commercial applications designers usually resort to cleaning systems based on artificial air purges to avoid optic deterioration. Due to space resource restrictions the GTS includes an in-flight calibration system with no moving parts, which accounts for the degradation of the sensor due to dust deposits on the thermopile's filter. The system is

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implemented by a high emissivity and low mass calibration plate; see Fig. 1, which can be heated to the desired temperature, using for that only 0.5W during 5 minutes. It is placed in front of the thermopiles' hosting piece, so that each thermopile faces the ground through a hole in this plate. In this way an annulus of the filter that represents part of the thermopiles' FOV is obstructed by the calibration system, limiting the solid angle measurement. The temperature of this plate, T p , is measured using a specific RTD glued to its surface. As far as the authors are aware, this is the first time a recalibration system like the one described here and without moving parts has been used in this way on a pyrometer. It is important to note the existence of potential applications on our planet, in relation to the specific characteristics of the GTS autonomous recalibration system. Some examples would be air condition systems or temperature monitoring of train and car wheels and brakes, in general commercial applications with intensive use of contactless temperature sensors where recalibration of individual sensors would imply a high cost. Also, environmental monitoring systems deployed in extreme and remote places with long working times, where access for recalibrating is complicated and expensive.

GTS thermal model

The proposed thermal model is based on an energy balance equation (1) that accounts for the heat in the thermopile bolometer coming from all the bodies around it, see Fig. 2a

s cb C s cb R s cc R s f R s p R s g R , , , , , , , (1)
P R and P C are terms that represent the heat exchanged between the bodies of the subscripts, through radiation, conduction and convection respectively. As the bolometer is designed to be well insulated from the can and to have low thermal mass, the thermal equilibrium condition of the equation ( 1) is reached after a setting time of a few milliseconds, which means

•K -1 •m -2 h Planck's constant, J•s c light velocity, m•s -1 k Boltzmann's constant, J•K -1 K p-c
thermopile's thermal gradient constant

K 1 , K 2 and K 3 sensor model constants, m 2 , m 2 , W•K -1 C bolometer heat capacity, J•K -1
Greek symbols part of the thermopile FOV not obstructed by the calibration plate Based on simplified one dimensional heat transfer models using the standard convection, conduction and radiation expression [START_REF] Incropera | Introduction to Heat Transfer[END_REF], in which it is assumed that the temperature of the atmosphere inside the thermopile is equal to that of the can base, T cb , and that thermal

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equilibrium is reached, equation ( 1) can be rewritten in (2). Heat flux terms x are calculated based on Planck's law. Two reasonable simplifications can be assumed in [START_REF] Escriba | Complete analytical modelling and analysis of micro-machined thermoelectric uncooled IR sensors[END_REF]. First, that the bolometer's FOV of the filter, which is limited by the shape of the thermopile can, is equal to the sum of the ground and calibration plate FOV, F s-f =F s-g +F s-p , see Fig. 2b, and second, the bolometer's FOV of the thermopile's can base and can cap are quite similar F s-cb ≈F s-cc since they represent almost the same approximate solid angle, 2 steradian2 .

0 ) •( • • 2 • )• •( • • • • • • • • • • s cb s c e e e s cc s cb s f s s cb cb s s cc cc s s f f s s p p s s g g s s T T A h d A F F F A F A F A F A F A F A (2)
Areas, FOV factors, conductivities, convection coefficient and effective length in (2) are initially unknown, and depend on specific parameters of the thermopile materials and their relative position inside the GTS. In order to simplify the process of identifying these terms they have been grouped together, obtaining as a result equation ( 3)

0 ) •( )• ( • 2 • 2 • • )• 1 ( • • 3 2 1 2 2 1 1 1 s cb s cb cc f p g T T K K K K K K K K (3)
where

K 1 =A s •(F s-g +F s-p ), K 2 = A s •(F s-cc + F s-cb )=, 2 • • •
5 2 1 • 2 ) ( • d e hc a g KT hc f s g g 0 5 2 1 • 2 ) ( • d e hc a p KT hc f s p p 0 5 2 1 • 2 )) ( ) ( 1 ( d e hc a f KT hc f f s f 0 5 2 1 • 2 d e hc s KT hc s s (4) 0 5 2 1 • 2 • d e hc a cc KT hc s cc cc 0 5 2 1 • 2 • d e hc a cb KT hc s cb cb
All these integrals depend on different temperatures: T cb and T p are directly measured using specific RTDs attached to the corresponding bodies. During the GTS calibration process the target temperature T g is measured by a specific contact temperature sensor, while during the normal operation it is the unknown to be measured by the GTS. The temperature of the filter is the same as the temperature of the thermopile's can cap as they are bound by a conductive adhesive T f =T cc . And the temperature of the thermopile's can cap is equal to the temperature of the thermopile's can base, T cc =T cb , since both are made of the same material (steel) and they are in good thermal contact, except when the in-flight calibration plate is being heated.

Finally, the temperature of the bolometer, T s , is obtained from the output voltage of the thermopile [START_REF] Grafa | Seebeck's affect of micro-machined thermopiles on infrared detection[END_REF] [START_REF] Foote | Temperature stabilization requirements for unchopped thermal detectors[END_REF]. The thermopile produces a voltage representation of the temperature difference between its can base (cold junction) and the bolometer (hot junction), equation [START_REF] Grafa | Seebeck's affect of micro-machined thermopiles on infrared detection[END_REF].

The GTS thermopiles have 100 thermocouples connected in series and embedded between the

•( • 100 cb s T AB out T T V C (5)
The GTS thermal model is completed with the thermopile's thermal gradients estimator. The calibration plate will be heated as part of the in-flight calibration process, generating a thermal gradient in the whole GTS and more specifically in the structure of the thermopile [START_REF] Boidens | International patent WO 2008/139321 A1, Infrared Radiometer[END_REF], Fig. 3.

As shown in Fig. 1, the calibration plate is attached with screws to the thermopiles' hosting piece. Thus, thermal coupling exists between these two pieces and by extension with the thermopiles, based on conduction, through the atmosphere, the screws, and radiation. In this way, a thermal gradient will appear between the thermopiles' can cap at the top and the can base at the bottom. From this, the proposed estimator takes into account the existence of a relationship between the difference in the temperature of the calibration plate before and after heating T p2 -T p1 , and the temperature gradient between the thermopile's can base and cap (6). Actually, the assumption of a constant over temperature for the whole can cap during the inflight calibration represents a simplification of the real situation. This relation is assumed to be lineal through the constant K p-c for a certain absolute temperature, since the non linear radiation term can be simplified in a linear term [START_REF] Foote | Temperature stabilization requirements for unchopped thermal detectors[END_REF].

) •( 1 2 p p c p cb cc T T K T T (6)
From analysis of equations ( 4) and ( 6), we can conclude the need to identify the unknown constants of the sensor model: K 1 , K 2 , K 3 , and K p-c .

Differential equations for REMS GTS model identification

In order to avoid the uncontrolled but constant heat flux terms derived from the experimental test setup, see Fig. 4, a differential procedure and analysis of the energy balance equation is applied. These undesired terms are: the blackbody environment reflections r , that arise because blackbody emissivity is different from one, and the IR window emissions and reflections, w . These heat flux terms appear in the energy balance equation ( 3), modifying it until it is converted into [START_REF] Ploteau | Conception of thermoelectric flux meters for infrared radiation measurements in industrial furnaces[END_REF], where w represents the cryostat window average transmittance.

0 ) •( )• ( • 2 • 2 • • )• 1 ( ) • •( • 3 2 1 2 2 1 1 1 s cb s cb cc f p r w g w T T K K K K K K K K (7)
The differential procedure combines two energy balance equations [START_REF] Ploteau | Conception of thermoelectric flux meters for infrared radiation measurements in industrial furnaces[END_REF] for pairs of blackbody or calibration plate temperatures with the same thermopile temperature. Thus, by subtracting the two energy balance equations, in which the temperatures of the cryostat IR window and the laboratory environment remain stable, the unknown but constant heat flux terms, w and r , are eliminated. A detailed analysis of this procedure is described in each test subsection.

Additionally, the differential procedure makes it possible to avoid errors caused by the constant thermal gradients on each thermopile's can, which may appear for each consigned thermopile temperature as the thermopiles' hosting piece is heated or cooled [START_REF] Liess | Stabilization of the output signal of thermopile sensors in the thermal environment of automotive applications[END_REF].

Tests and results

This section includes the description and analysis of a series of three tests the objective of which is to identify the sensor model constants K 1 , K 2 , K 3 , and K p-c , that are part of the GTS instrument calibration plan. Additionally, a test designed to show ability to measure the temperature of the target is also included.

The results shown in the following subsections have been obtained from a GTS engineering model constructed for test purposes and a thermopile with a band pass filter of 8 to 14 m, see Electronic Annex 1 in the online version of this article. Table 1 summarises the test conditions and the temperatures consigned to the different GTS elements. In the case of the identification tests, sampled variables are only collected after the consigned temperatures are stable. 2 summarizes the average practical value for the emissivities of the different bodies, and for the filters transmittance and reflectance, under the hypothesis of greybody behaviour.

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Blackbody and calibration plate emissivities, ε g and ε p , are computed from spectral data of the corresponding surfaces, taking into account the form of Plank's law for the tested temperatures.

From spectral data, it can also be said that the cryostat KRS-5 window χ w and the thermopile window χ f ( ) present a plain spectral transmittance inside the band-pass. Bolometer absorptivity a s and emissivity s are vey high, since it is cover with a high emissivity coating (Ag-black), but its exact value has not been tested. As approximation, it is assumed that both are equal to 1.

Finally, we have the emissivities of the inner side of the thermopile's can, ε cc and ε cb , and the thermopile's filter inner side reflectance, ) ( f . IR filters like the one of the thermopile present high reflectance outside the band pass, while in the band pass the reflectance is very low.

Additionally, the filter diameter (2mm) is relatively small versus the thermopile's can diameter (8mm). So, the thermopile's can and the filter form almost a closed structure. In addition to that, both elements have the same or quite similar temperature. Therefore, considering the internal reflections inside the thermopile's can, the whole structure behaves as a cavity blackbody, which is supposed to have a very high emissivity. As a result of the former, filter reflectance is assumed to have a null value, while thermopile's can emissivity is approximated to 1. To carry out this first test the calibration plate has been removed, ensuring that =1. In addition, because the test is carried out in homogeneous temperature conditions without heating up the calibration plate, the temperature in the thermopile base, cap and filter are equal, T cc =T cb =T f . Nevertheless, if there is any thermopile spatial thermal gradient its effect is avoided because of the differential analysis. From these premises the energy balance equation ( 7) can be rewritten,

0 ) •( )• ( • 2 • 2 • ) • •( 3 2 1 2 2 1 1 s cb s cb cc f r w g w T T K K K K K K K ( 8
)
From equation ( 8) and for the pairs of blackbody temperatures in table 1, with the same or fairly similar thermopile temperature, as from a practical point of view keeping the thermopile at exactly the same temperature is impossible, the differential analysis results in,

0 ) •( ) )•( ( ) •( 2 ) •( 2 ) •( ) • • •( 2 1 2 1 3 2 1 2 1 2 1 2 2 1 2 2 1 1 2 1 1 s s cb cb s s cb cb cc cc f f g w g w T T T T K K K K K K K (9)
The identification of K 1 , K 2 and K 3 is achieved based on equation (9) and a linear least square algorithm that tries to minimize the estimation error. To carry out the algorithm it is necessary to know the calculations of the heat flux terms based on (4) and the temperature measurements of the whole set of thermopile and blackbody temperature references in table 1. As a result, assuming that the value of K 1 =1, the relative values of the constants K 2 and K 3 , are obtained. Table 3 summarizes the results of the process, including the root mean square error associated with the estimation of blackbody temperatures, while Fig. 6 graphically presents specific results.

Test for identification of

In this test the calibration plate is mounted on the front of the thermopile and the values of the previously identified constants K 1 , K 2 and K 3 are required. The test consists of setting different temperatures for the blackbody, table 1. As the temperature of both the thermopile and the calibration plate are stable the temperature in the thermopile base, cap and filter are equal, T cc =T cb =T f . A differential analysis of the energy balance equation for two different blackbody temperatures can again be applied to [START_REF] Ploteau | Conception of thermoelectric flux meters for infrared radiation measurements in industrial furnaces[END_REF],

0 ) •( ) )•( ( ) •( 2 ) •( 2 ) •( ) •( )• 1 ( ) • • •( • 2 1 2 1 3 2 1 2 1 2 1 2 2 1 2 2 1 1 2 1 1 2 1 1 s s cb cb s s cb cb cc cc f f p p g w g w T T T T K K K K K K K K (10)
and finally equation (10) can be solved for ,

) •( ) • • •( ) •( ) )•( ( ) •( 2 ) •( 2 ) •( ) •( 2 1 1 2 1 1 2 1 2 1 3 2 1 2 1 2 1 2 2 1 2 2 1 1 2 1 1 p p g w g w s s cb cb s s cb cb cc cc f f p p K K T T T T K K K K K K K (11)
The individual and average values of as a result of applying equation [START_REF] Incropera | Introduction to Heat Transfer[END_REF] to the set of temperature references of table 1 are shown in Fig. 7. Table 3 summarizes the average value of and the associated root mean square error in the estimation of blackbody temperature.

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Test for identification of thermopile thermal gradient constant K p-c

This test is designed to establish a relationship between the increase in the temperature of the calibration plate and the thermal gradient generated between the thermopile's can cap and base, T cc -T cb . In the case of this test, window reflections cannot be avoided by using a differential analysis of the energy balance equation as the differential analysis is developed for different calibration plate temperatures and so the reflections are different for each test point. Thus, the setup of the test has been slightly modified, removing the cryostat window χ w =1, in order to eliminate these window reflections.

The test consists mainly of setting different temperatures for the calibration plate, using for this the associated heater. While the temperature of the blackbody remains constant, the temperature of the thermopile changes freely due to the heat coming from the calibration plate.

The aim of this procedure is to emulate the appearance of thermal gradients on the thermopile's can due to the in-flight calibration algorithm running during Martian operations.

Once again, from the energy balance equation [START_REF] Ploteau | Conception of thermoelectric flux meters for infrared radiation measurements in industrial furnaces[END_REF], in which the value of the constants K 1 , K 2 , K 3 and have previously been identified, a differential analysis is applied in order to avoid the error term r . Equation [START_REF] Liess | Stabilization of the output signal of thermopile sensors in the thermal environment of automotive applications[END_REF] represents the result of the differential procedure for two different calibration plate temperatures. The first temperature, in which the calibration plate is not heated, is used as a reference point and so it is assumed that T cc1 = T f1 =T cb1 . In this way equation ( 12 The result of applying equation [START_REF] Liess | Stabilization of the output signal of thermopile sensors in the thermal environment of automotive applications[END_REF] to the set of temperatures in table 1, taking several pieces of data for each calibration plate temperature is shown in Fig. 8. The figure shows the linear regression (6) between the calibration plate over-temperature and the thermopile thermal gradients through the constant K p-c , the value of which is shown in table 3. As it demonstrates, practical data validate the lineal model of the thermal gradient (6). Despite the relatively small value of the thermopile thermal gradient, which is between 0.01-0.023ºC, its relevance in target temperature determination is important as principally it modifies the heat term 9, consists of sampling GTS temperature variables for 100 minutes with a sampling period of 1 minute, after 30 minutes the temperature of the calibration plate is increased using the associated heater in order to simulate the running of the in-flight calibration algorithm, while the temperature of the thermopiles evolves freely, table 1. In order to estimate the temperature of the blackbody, energy balance equation ( 7) must be solved for g [START_REF] Boidens | International patent WO 2008/139321 A1, Infrared Radiometer[END_REF] and after that by using numerical methods for T g . This procedure is not differential, and in order to avoid the errors caused by the emissivity of the blackbody that differs from one ε g ≠1 and reflections from the environment, the selected temperature of the blackbody is equal to the temperature of the environment, thus the blackbody's emissivity can be assumed to be ε g =1. Additionally, the cryostat window has been newly removed in order to eliminate window influence w , which means that χ w =1. To correctly estimate the blackbody's temperature while the calibration plate is being heated, equations ( 6) and ( 7), means a reference value for T p must be taken so the calibration plate over-temperature can be determined and from it the value of T cc and T f . The reference has been established at the 30 th minute.

) •( ) )•( ( ) •( 2 ) •( 2 ) •( ) •( )• 1 ( 2 1 2 1 3 2 1 2 1 2 1 2 2 1 2 2 1 1 2 1 1 s s cb cb s s cb cb cc cc f f p p T T T T K K K K K K K (12)
1 3 2 1 2 2 1 1 • ) •( )• ( • 2 • 2 • • )• 1 ( K T T K K K K K K K s cb s cb cc f p g (13)
where

cb p p c p f cc T T T K T T ) •( m in 30 , M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT
The results of applying equation [START_REF] Gomez-Elvira | REMS, an instrument for Mars Science laboratory Rover[END_REF] for the whole set of data are shown in Fig. 10, where the real and estimated blackbody temperatures are plotted. Data present a root mean square error of 0.1032ºC, which is within the calibration boundary error of the RTDs used in the test and is compliant with REMS GTS requirements. For a few minutes after the process of heating and cooling the calibration plate has started the estimation error is higher. This is due to the temporal thermal gradient of the thermopile's can [START_REF] Liess | Stabilization of the output signal of thermopile sensors in the thermal environment of automotive applications[END_REF], which as temperatures have not reached a stable state, the calibrated value of K p-c cannot be assumed.

Conclusions and future work

This paper proposes a new simplified mathematical model for the REMS GTS sensor, which can be applied to similar pyrometers. Unlike simpler models, this one is based on the thermal and electrical operation of the thermopile and the physical structure of the sensor. To demonstrate the performance of the model, practical results are provided with the aim of showing: Firstly, the validity of the proposed model and methods for characterising the REMS GTS, due to the low least-squares error presented during the different calibration tests, and secondly, the capability of measuring the temperature of a target with a root mean square error below 0.15ºC, compliant with sensor specifications.

Despite the relatively simple model proposed, the actual physical situation is more complicated. In the identification of K 1 , K 2 and K 3, aspects such as, thermopile's can thermal model, thermopile filter transmittance variation versus temperature and the appearance of inner temperature gradients in thermopile elements may warrant additional consideration being given Despite the fact that the identified value of K p-c is constant and depends on the thermal coupling between the calibration plate and the thermopile's hosting piece, it may also depend on the thermal coupling between the entire GTS and its support structure. In addition, atmospheric conditions and the absolute temperature may also be important to the value of K p-c , as they modify thermal coupling through atmosphere conduction and radiation. Once again, to sum up we could say that the K p-c constant of the REMS GTS flight model must be calibrated with the GTS located in its end position inside a test chamber filled with a Martian like atmosphere and taking into account the absolute temperature working range. Depending on the absolute temperature, this may imply obtaining different values for K p-c ,.

  thermopile and the geometrical disposition, mass and volume of the sensor elements. The objective is to calculate and design the sensibility and time response of the sensor based on the value of these parameters.

  a) The 3D mechanical layout of REMS GTS, (b)The 2D mechanical layout of REMS GTS and a thermopile.

  heat exchanged between bodies x through radiation, W P Cx-x heat exchanged between bodies x through conduction and convection, W T x temperature of the body x, K F s-x field of view factors between the body x and the bolometer A s area of the bolometer, m -2 A e effective section of the materials between the bolometer and the can base, m -2 d e effective length of the materials between the bolometer and the can base, m h c convection coefficient of the thermopile inner atmosphere, W

f 1 x

 1 thermopile filter transmittance vs. wavelength f thermopile filter reflectance vs. wavelength w cryostat window average transmittance wavelength, m e effective thermal conductivity between the bolometer and the can base, W•K -1 •m -

  Fig.2 (a) Thermal diagram of sensor exchanged heat, (b) Diagram of sensor field of view.

  show the way in which the heat flux terms are calculated, integrating Planck's law. The expressions consider that an incoming radiation becomes a heat gain through the M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT absorption phenomenon in thermopile's bolometer, taking into account the average value of bolometer absorbance a s . They also include the average emissitities of different bodies, assuming the hypothesis of greybody behavior for all of them. Finally, thermopile filter transmittance ) ( f is taken into account to calculate the flux terms inside filter transmission band for those elements outside the thermopile structure, and filter reflectance ) ( f is also considered to work out the flux term radiated by the filter inside and outside the transmission band.

  0

  M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT can and the bolometer, and the term cb T AB stands for the Seebeck coefficient related to the association of the two materials of the thermopile's thermocouples.

)

Fig. 3

 3 Fig.3GTS and the thermopile's thermal gradient.

Fig. 5 REMS

 5 Fig.5 REMS GTS tested model.

Fig. 6

 6 Fig. 6 Blackbody temperature estimation associated with the identification of K 1 , K 2 and K 3 .

Fig. 7

 7 Fig.7 Experimental data for ground relative FOV , as a function of T g .

cc and 2 f

 2 for the unknown temperature T cc2 , which is equal to T f2 , from the value of 2 using numerical methods. The other temperatures and heat flux terms are all known.

  0

Fig. 8

 8 Fig. 8 Experimental data for thermopile thermal gradients constant estimation K p-c .

4 . 4 .

 44 weighting in the energy balance equation. Test of sensor performance This final test, which is not part of the instrument calibration plan, is designed to analyse the behaviour of the proposed model in the estimation of blackbody temperature, taking into account the identified values of model constants. The test aims to recreate the temperature measurement process on Mars and in this way its setup is shared with the previous test, M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 16 removing the cryostat window. The test, see Fig.

Fig. 9

 9 Fig. 9 Evolution of temperatures during the sensor performance test.

Fig. 10

 10 Fig. 10 Blackbody temperature estimation.

  variation versus temperature and the calibration set-up. This implies that the identification test for these constants must be run covering the Martian REMS GTS working temperature range, and the values of these constants may be different for different temperature ranges within this working range.

  Figure 1a

Table 1

 1 Test summary of experimental temperature references and test conditions

	Test	Blackbody temperature T g	Thermopile temperature T cb	Calibration plate temperature T p	Cryostat atmosphere
	Identification of Ks	~[40, 60,... 120]ºC	~[-10, 0, 10,… 40]ºC	-	Vacuum
	Identification of	~[40, 60,... 120]ºC	~40ºC	~40ºC	Earth atmosphere
	Identification of thermopile thermal gradient K p-c	~23ºC	~23-28ºC	~Tcb +[0, 9, 13, 18]ºC	Earth atmosphere
	Test of sensor performance	~23ºC	~23ºC	~Tcb +[0, 11]ºC	Earth atmosphere

Table

Table 2

 2 Practical data required for heat flux terms calculations

	Variable	Value
	ε g	0.9433
	ε p	0.9018
	ε cc	1
	ε cb	1

. Identification test for K 1 , K 2 and K 3

Table 3

 3 Calibration test results

	Variable	Value	Target temperature error RMS
	K 1	1m 2
	K 2	23.6095m 2	0.0529ºC
	K 3	133.0812W/K
		0.6605	0.0287ºC

This assumption takes into account the small size of the filter, 2mm, versus the 8mm of thermopile diameter F s-f << F s-cb .

Acknowledgements

This work forms part of the research project regarding the design and scientific issues of the NASA/MSL REMS. The authors would like to express special thanks to all REMS Co-Is, collaborators and the INTA Metrological department, who participate in a variety of ways to the development of REMS GTS, as well as the referees and their fruitful contributions. Also acknowledge the financial support provided by the Spanish institutions CYCIT through the ESP2007-65862 grant and CDTI.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT


R Boukhanouf
email: rabah.boukhanouf@nottingham.ac.uk

A Haddad

A CFD Analysis of an electronics cooling enclosure for application in telecommunication systems

Keywords: Electronics cooling, CFD, Flotherm, RF components, heat spreader

This paper presents results of CFD analysis of an electronics cooling enclosure used as part of a larger telecommunication radar system. An original cooling enclosure was simulated using Flotherm which results were taken as the benchmark thermal performance. It was found that the operating temperature of one of the Radio Frequency (RF) components will exceed the design temperature limit of the PCB. A solution involving a re-design of thermal spreading arrangements using a 3 mm thick copper shelf and a Vapour Chamber (VC) heat pipe was found to bring the operating temperatures of all RF components within the specified temperature limits. The use of a VC, in particular, reduced the 60W RF component steady state temperature by an average of 5.4 o C. The study also shows that increasing the finned heat exchanger cooling air flow rate can lower further the RF components temperature though at the expense of increasing energy consumption of the fan.

Introduction

The trend for densely populated printed circuit boards (PCB) and high processing speeds of power electronics and telecommunication systems has created a real challenge to develop sustainable thermal management solutions [START_REF] Reay | Heat Pipes: Theory, Design and applications[END_REF]. The problem resides in finding efficient ways of temperature control and heat removal both at the chip and rack level of packaged systems for the safe and reliable operation. A large number of research studies in thermal management of electronics have been conducted. For example, Nnanna [START_REF] Agwu Nnanna | Application of refrigeration system in electronics cooling[END_REF] studied the use of vapour compression refrigeration systems for electronics cooling where the study focused on transient response to fluctuation in applied load. However, long time response of the thermal expansion valve contributed to heat build up at the chip level resulting in high thermal stress. Lee et al. [START_REF] Lee | Package embedded heat exchanger for stacked multi-chip module[END_REF] looked at embedded heat exchanger for stacked multi-chip module using polymer materials. However poor thermal conductivity of the material necessitated the deployment of a thin silicone film (Polydimethylsiloxane, referred to as PDMS) between the chip and the micro-channel. Schmidt and Shaukatullah [START_REF] Schmidt | Computer and telecommunications equipment room cooling; a review of literature[END_REF] investigated different cooling strategies in telecommunication systems through numerical and experimental work. The focus was on cooling and energy saving techniques.

Leung et al. [START_REF] Leung | Horizontal simulated printed-circuit board assembly in fully-developed laminar-flow convection[END_REF] worked on experimental and numerical prediction of heat transfer characteristics by convection of a horizontal PCB assembly subjected to fully-developed laminar-flow. It was found that most of heat transfer occurred at the top surface of the PCB.

RF power amplifiers components usually operate under severe conditions of high power dissipation and consequently high junction temperatures which may lead to poor reliability and ultimately premature failure of components [START_REF] Radivojevic | Operating limits for RF power amplifiers at high junction temperatures[END_REF]. New generation of telecommunication systems employ high power RF amplifiers and close packing of PCB which renders forced conviction air cooling alone ineffective to operate at prerequisite temperatures. Hence methods of fast heat conduction and spreading are often employed to remedy this problem.

Usually, solid metal such as copper and two-phase heat pipe thermal base are employed to enable high heat flux transfer from a heat source level to the heat sink. Vapour chamber heat pipes, in particular, are being developed as mounting surfaces for multiple heat sources for heat spreading over a large surface to eliminate thermal hot spots [START_REF] Boukhanouf | Experimental investigation of a flat plate heat pipe performance using IR thermal imaging camera[END_REF]. Heat pipes can also be used to conduct heat far away from the heat source and be located at the chip or rack level to control the temperature in for example telecommunication cabins. This paper investigates arrangements to improving thermal performance of an original cooling aluminium enclosure used in telecommunication systems through CFD analysis.

The investigation includes the use of solid copper as well as vapour chamber heat pipes as supporting shelves for electronic PCBs.

Description of the benchmark electronics cooling system

The presented RF components cooling system was built as part of a larger telecommunication control system, which would contain hundreds of such units. However, for the purpose of this analysis, only one cooling enclosure unit would be considered here.

As shown in Figure 1, each unit was made up of a 55 x 55 mm sealed aluminium enclosure that houses two PCBs located on two separate shelves. Four heat generating electronic chips with varying heat load ratings were supported: one DC power electronic component of 15 W located on the upper shelf and three RF components mounted on the lower shelf with one component rated at 60 W and two other identical components each rated at 0.5 W.

In the original design, the PCBs were mounted on a 1 mm copper base material to conduct heat generated in the electronic component to the aluminium enclosure. As well as being a heat sink, the enclosure is also used as a shield to protect against electrical interferences with the RF components circuits. Hence heat transfer from the electronic components to the enclosure occurs through conduction only. A fan and an aluminium finned heat sink assembly was mounted onto the enclosure base to reject heat through forced air convection.

To minimise energy consumption of the fan, a speed controller was used to adjust the speed of the fan to deliver accurately the required cooling air flow rates and maintain operating temperature of the 60 W RF components in particular within the design specifications. The power consumption of the fan ranged from 0.03 W, when the electronic components were in standby mode, to 0.5 W at full operation mode which results in high heat rejection rates through the finned heat exchanger. The main steady state operating parameters of the forced air cooling enclosure is shown in Table 1.

CFD modelling of the Benchmark system

CFD modelling and simulation has become a routine design tool for predicting accurately thermal performance of electronics cooling systems. The simulation can be a fast and cost effective method to evaluate and optimise heat transfer processes in a wide range of prototype geometries and working conditions. For example, CFD can be used to map temperature distribution on a mounting surface of a PCB with a varied heat generating components and highlight areas where the junction temperature of the semiconductor components could be above the maximum safe temperature specified by the manufacturer.

Currently, there are a number of competing commercial CFD packages that can be used, though Flotherm and Icepak are the two main popular packages that are designed specifically for predicting fluid flow and heat transfer in electronic cooling systems [START_REF] Yang | A comparison of using Icepak and Flotherm in electronic cooling[END_REF].

Flotherm is a finite volume based software package that uses simple Cartesian grid meshing. It has a 3D solver for Navier-Stokes equations and equipped with built in boundary conditions for common heat transfer devices and a capability to take into account turbulent flow viscosity losses. The restriction to Cartesian grid meshing, though may enhance convergence, generates a larger grid density. Similarly, Icepak is a finite volume based software package but with much more mesh control capability, enabling meshing of irregular object surfaces. Both packages have a user friendly interface and large library of predefined thermal models for common electronic components/objects such as fans, CPUs, heat sinks, enclosures, PCBs, thermal interface contact resistances, and air flow patterns. This enables fast and accurate design studies to be implemented with detailed graphical information on temperature distribution, fluid flow rates and pressures.

Yang [START_REF] Remsburg | Advanced thermal design of electronic equipments[END_REF] showed that both Icepak and Flotherm can yield accurate modelling results for heat transfer in electronics cooling application for laminar and turbulent regimes. However, good knowledge and expertise of heat transfer processes coupled with experimental data may be required to ensure good prediction of results.

In this research, Flotherm was chosen for the design of different cooling strategies of the RF components enclosure. This rectangular shape of the enclosure, shelf components and mounting supports, lend themselves well to meshing using Cartesian coordinates and hence to the use of Flotherm with added advantage of fast converging solution.

In this work, the CFD analysis using Flotherm was first conducted on the benchmark system to determine the baseline operating properties. Figure 2 shows a 3-D CFD model of the enclosure and associated component shelves and heat sink. The analysis consists in determining steady state thermal performance of the enclosure, shelves and heat sink to conduct heat away from the heat generating components and maintain a tolerable operating temperature. A Flotherm built-in standard PCB tool was used to model the electronic components. In this tool, the board material and various thermal resistances along the heat transfer path can be specified. All the components were considered to have a layer of solder as an interface with the mounting board. In addition, a thin layer of thermal conductive interface material (Sil Pad ® and Gap Pad ® TIM) with a thermal conductivity of 2.0 W/mK was specified for the interfaces between the PCBs, copper shelves, the enclosure frame and the heat sink. A summary of all materials and their operating properties used in the CFD analysis are given in Table 2.

DC shelf

Figure 3 shows a 3D CFD model of the DC shelf and its cross section. The PCB material was made up of a woven fibreglass material and impregnated with a Flame Retardant 4 (FR4) material. This grade of PCB material is manufactured from multilayer glass fibre epoxy laminates bonded together and has a thickness of 1.6 mm and a glass transient temperature of 135 o C [START_REF] Coppola | Investigation on current density limits in power printed circuit boards[END_REF]. FR4 is a stronger substrate and resistant to cracking or breaking with excellent manufacturing and operating characteristics. It is usually found in higher end electronics and is readily available on short lead-time [START_REF] Arulvanan | Assembly and reliability of PBGA packages on FR4 PCBs with SnAgCu solder[END_REF].

An array of copper plated thermal vias was incorporated into the RF4 PCB material directly underneath the DC power electronic component. The copper plated thermal vias occupy an area of 19 x 14 mm and serve to augment heat conduction from the heat source to copper base below the PCB. The thermal resistance of an individual via can be calculated from the via radius, the via length between the heat source and the copper spreader plate, and the plating thickness [START_REF] Coombs | Printed Circuits Handbook[END_REF][START_REF] Setty | Commercial-off-the-shelf MMIC components offer high reliability[END_REF]:

( ) 2 1 2 r r k l R o via via - = π (1)
where r o is the via drill radius, r 1 the via inner radius, l via the via length, and k the thermal conductivity of copper. The effective thermal resistance of the via array can be calculated from individual thermal resistances connected in parallel. This is given as:

∑ - = n i via eff R R 1 1 1 (2)
Using equation 1 and 2, the effective thermal resistance of the via array can be calculated.

Therefore inserting the number of vias of 187, the length of 1.6 mm, diameter of 0.8 mm and a plating thickness of 0.05 mm, Equation 1 and 2 yield as a first approximation the thermal resistance of an individual via and the via array of 35.27 o C/W and 0.19 o C/W respectively. In addition the effective thermal conductivity of the entire area, A, under the DC power electronic component can be evaluated as:

A R l K eff via eff × = (3)
Using equation 3, the effective thermal conductivity of the area with thermal via array is approximately 31.65 W/mK. This represents a large improvement compared to the PCB thermal conductivity of 0.6 W/mK

RF components lower shelf and heat sink

The RF components were located on the lower shelf (i.e., the base) of the enclosure to which a finned aluminium heat sink was attached. Figure 4 show a 3D CFD model of the lower shelf and heat sink assembly and a cross of the assembly respectively. As can be seen from the figure, the heat generated from the RF components needs to be conducted through three different layers before it can be rejected away in the 1 mm thick copper spreader: a thin solder layer, an aluminium PCB and a TIM. A layer of a dielectric material above the aluminium PCB was deployed to ensure good electrical isolation of the electronic circuits.

The dielectric material has a dielectric constant in the range of 4.1 to 4.2 and a dissipation factor of 0.019 to 0.024. There are no thermal vias used in the lower shelf PCB.

The heat sink was modelled using Flotherm heat sink smart part, which allows specifying the dimensions of the base, fin height, pitch, and thickness. The heat sink CFD model employed a grid of at least three cells between each fin to enable enough resolution for the solver to develop accurate temperature profiles. The fan speed was adjusted so that it can deliver a constant volumetric flow rate of 11 m 3 /h at a pressure difference of 4 Pa and a cooling air temperature of 40 o C. In this analysis, it was assumed that heat transfer by radiation is negligible.

Benchmark model CFD results

The steady state thermal performance analysis of the electronics enclosure with respective heat sources operating at full load was performed using Flotherm. The main consideration was to identify that the temperature limits of the DC and RF components PCBs were not exceeded under the benchmark operating conditions. Figure 5 shows a front view section of the enclosure temperature gradient slicing through the DC power electronic component.

It can be seen that the highest temperature occurred at the DC component with a maximum of about 101 o C. Though this is slightly below the maximum allowed operating temperature limit of 110 o C, as specified in Table 1, nevertheless it is still high for safe and steady state operation. Finally, the heat conducted to the enclosure casing must be rejected away through the fan heat sink assembly. The energy consumption of the fan is directly related to the pressure drop and air flow rate. Hence the airflow velocity and pressure drop in the finned heat exchanger was modelled using Flotherm. Figure 7 shows simulation results of cooling air speed fields as it travels through the heat sink fins. It can be seen that the maximum air flow speeds are found at the base of the heat sink inlet (red arrows) as cooling air is circulated across the narrow heat sink fins by a fan. Similarly, Figure 8 shows a mapping of air flow pressure distribution in the heat sink with expected high pressure drops occur near the air inlet at the heat sink base.

From the above results, it became clear that the benchmark design needs significant improvement to the heat dissipation process that prevents excessive overheating and ultimately failure of the electronic components. Hence the following section describes the design changes to the heat transfer elements and the thermal merit of each alternative.

Design Improvements

Taking the benchmark design as the starting point, the effect of the following design strategies were assessed using CFD analysis. Throughout the CFD analysis, the cooling air flow rate of the electronics enclosure heat sink and the ambient air temperature were held constant at 11m 3 /h and 40 o C respectively. All CFD simulation results are summarised in Figure 9 for all the design options given in the following sections with

Effect of increasing the RF components copper base plate thickness

In the benchmark model, the heat generated by the 60 W RF component created a hot spot on the PCB with a temperature higher than the PCB's temperature limit of 135 o C. As a first option, the effect of increasing the thickness of the copper base plate from 1 mm to 3 mm was considered. This should aid to spread and conduct heat more effectively from the heat source to the heat sink. The CFD simulation results of this design are given in column three of Figure 9. It is shown that little effect on the temperature of 60 W RF component had been achieved. This in effect was still about 2 o C above the PCB's maximum operating temperature. On the other hand, the temperature of all other RF components on the same PCB was in compliance with the design specification.

Effect of replacing the RF components copper base plate with a 3 mm thick

Vapour Chamber

Advanced thermal management solutions in electronics cooling often employ a two-phase fluid for heat transfer using heat pipes. These are high heat conduction devices that take advantages of latent heat of a working fluid as it undergoes phase change. A standard tubular heat pipe is usually the simplest and cheapest configuration of such as a device.

However, for this application, shape adaptation to accommodate the flat mounting surfaces of electronic components would be required using for example a flat copper or aluminium solid plate onto which a PCB can be place on. This would defeat the purpose of using a heat pipe as an effective heat transfer mechanism. Therefore, more specialised heat transfer devices as a direct substitute for the solid mounting copper base such VC, also known as flat plate heat pipe, could be more effective.

A VC is made up of a sealed flat thermal conductive shell such as copper onto which an electronics PCB can be mounted directly. Heat generated from the multiple electronic components, which were assumed to be uniformly heat source, is then conducted away from the evaporator surface to the condenser. VCs have the advantage of spreading heat over the entire evaporator surface eliminating hot spots appearing under single heat generating components. The proposed VC schematic for this paper is shown in Figure 10, where it can be seen that there are two 0.5 W and one 60W heat generation rate RF components mounted on the evaporator surface. The inner wall of the evaporator has a sintered layer of wick material that is saturated with water as the working fluid.

The design of a VC is greatly dependent on a specific thermal application and the proposed VC modelling was carried out using Flotherm simulation package. The simulation combines both thermal and hydraulic properties of the VC. The thermal part defines the heat transfer from the RF components to the VC working fluid (water) and then from the working fluid to the condenser. The heat transfer from the evaporator into the VC causes the working fluid to evaporate off the sintered wick layer and the vapour to condense on the condensers surface with resulting heat being conducted away thorough the condenser wall.

Similarly, the hydrodynamic simulation characterises the working fluid flow in the wick as it is returned from the condenser to the evaporator through the acting capillary forces. It was assumed that the working flow in the wick is in laminar regime.

The Flotherm model was built using Standard Cuboids and Prism elements for the VC copper shell of 55 x 55mm and 3 mm thick, a 0.5 mm wick layer and a vapour space of 1mm high. Then Resistance Object model was used to define the thermal properties of each object. This is a useful tool where the thermal resistance of an object can be inserted manually or determined from other thermal parameters of the object such as thermal conductivity and heat transfer coefficients. It is established that the thermal resistance of the wet wick layer is the most significant resistance for heat transfer in a VC [START_REF] Liou | Visualization and thermal resistance measurement for the sintered mesh-wick evaporator in operating flat-plate heat pipes[END_REF].

Experimental tests at Thermacore Inc [START_REF] Grubb | CFD Modeling of a Therma-BaseTM Heat Sink[END_REF] and elsewhere has found that the effective thermal conductivity of the liquid saturated wick is an order of magnitude less than bulk wick material. For example a copper/water sintered wick layer has conductivity of about 10% that of bulk copper material (i.e., an effective thermal conductivity of 40 W/m K) [START_REF] Grubb | CFD Modeling of a Therma-BaseTM Heat Sink[END_REF][START_REF] Chen | Numerical simulation of a heat sink embedded with a vapor chamber and calculation of effective thermal conductivity of a vapor chamber[END_REF]. On the other hand, the temperature drop associated with the vapour flow could be assumed to be negligible, resulting in a high thermal conductivity of the vapour channel. In the current model an effective thermal conductivity of the vapour space was assumed to be 30,000 W/mK, though similar studies suggest that a thermal conductivity of approximated as 50,000 W/m K can be used [START_REF] Grubb | CFD Modeling of a Therma-BaseTM Heat Sink[END_REF].

The results of the CFD simulation with a VC was used as a mounting shelf of the RF components PCB are presented in column 4 of

Effect of replacing the enclosure shelves with VCs

The improvement to heat transfer of the electronics enclosure provided by the VC in the previous design led to considering the use of a VC unit for the DC shelf as well. The CFD simulation results for this case, presented in the last column of Figure 9, however show that only about 2 o C in temperature drop of the DC shelf would be achieved while the temperature of the FR components was unaltered. This suggests that incorporating an advanced spreading VC device to remove heat from the 15W DC component located on the top shelf is not cost effective.

Hence a further investigation was considered to assess the effect of increasing the heat sink airflow rate. For a comparative study, this was conducted for an enclosure with a 3 mm copper and a 3mm VC mounting base for the PCB of the RF components.

Effect of increasing enclosure heat sink airflow rates

Simulation results of varying airflow rate over the aluminium heat sink fins was conducted in a similar way as described previously. This was achieved by controlling the speed of the heat sink fan to increase the airflow rate by equal increments of 3 m 3 /h from the benchmark case of 11 m 3 /h to a maximum of 23 m 3 /h. This shows that the cooling air flow rate of the benchmark model was not adequately optimised, resulting in RF components having temperatures above the PCB's operating temperature limit. Increasing the enclosure heat sink air flow rates was however accompanied by an increase in fan power from 0.07 in case of the benchmark model to 0.4 W for flow rate of 23 m 3 /h , that is 22.5 % increase in energy consumption.

A similar simulation was performed for the case of substituting the copper shelf with a VC shelf. The results of this simulation are shown in Figure 12. It is shown that a similar trend of decreasing the temperature of all RF components with increased air flow rates was observed. Consistent with results obtained in the benchmark case for flow rate of 11m3/h, the VC exceeded the thermal performance of the solid copper shelf at all flow rates. For instance, at flow rates of 23 m 3 /h, the operating temperature of the powerful 60W RF components dropped to 116.5 o C which is 18.5 o C below the PCB maximum operating temperature. This shows that the overall thermal performance of the VC shelf unit is marginally better than the 3mm solid copper base for all flow rates. The operating temperature of the RF components was on average 5.4 o C lower when mounted on a VC shelf.

The thermal performance of a VC is application specific; however the evaporation and condensation process of the working fluid ensures a faster energy transfer from the heat generating electronic components to the heat sink, with the liquid flow in the wick contributing to spreading evenly the heat over a larger area. Previous research works showed that VC use as advanced thermal management solution in electronics cooling has always outperformed solid copper or aluminium materials of similar dimensions. Sonan et al. [START_REF] Sonan | Transient thermal and hydrodynamic model of flat heat pipe for the cooling of electronics components[END_REF] studied the transient performance of a 40 x 40 x 0.9 mm flat heat pipe used to cool multiple electronics components. A solid copper base of similar size was used to compare the cooling capability of the VC and it was shown that the maximum temperature difference between the hottest electronic component and the condenser was higher on the copper plate than on the VC by 11 K. The authors' previous work on large VCs [START_REF] Boukhanouf | Experimental investigation of a flat plate heat pipe performance using IR thermal imaging camera[END_REF] showed that on most cases VCs outperform solid copper as a mounting base for cooling electronics.

The authors found that the VC has the ability to generate a more uniform temperature distribution across the evaporator surface than the solid copper plate and measured temperature difference at the component level of up to 15 o C higher on solid copper plate that on a VC.

The thermal cooling performance improvement brought about by substituting the solid copper shelf by a VC in this work was marginally lower than that reported in previous work.

However, it is difficult to make exact comparison as testing and operating the VC may not be carried out under similar conditions. For example heat transfer from the electronic components to the heat sink occurs through a PCB, TIMs and the enclosure wall, increasing the overall thermal resistance. Furthermore, imposed ambient cooling air temperature of 40 o C as a design constraint had a limiting effect on rate of heat removal from the heating generating RF components.

CFD simulation accuracy

A mesh sensitivity analysis was performed in order to determine the accuracy of the results of the Flotherm simulations. This was carried out by varying the mesh density of a typical CFD model with 250,000 mesh counts. Two mesh counts of 35,000 and 500,000 were considered for which simulation solutions in terms of RF component temperatures are given in Table 3. It is shown that compared to the typical mesh count model (column 4), the high mesh count simulation results were 0.126 o C higher whereas for the low mesh count the difference was 3.608 o C, an accuracy range of 0.1% to 2.90%. Hence there is little to be gained by increasing the mesh count to 500,000 mesh counts as this will required more computation resources and processing time.

Conclusions

This paper presented a CFD simulation of an electronics enclosure cooling system to be used as part of a larger radar control system. The device contained two PCBs housed within an Aluminium enclosure with each PCB mounted on a copper shelf to help spread heat generated from the RF components. The highest power rating RF component was rated at 60 W and located on the lower shelf of the enclosure, which in turn was in contact with a forced air convection aluminium heat sink. The top shelf (DC component) houses a 15W power electronic component.

A parametric performance investigation showed that the original design was unsatisfactory, as the 60W RF component operating temperature exceeded the maximum limit safe limit of the PCB. Therefore, improved designs were suggested and the impact of each design variant on thermal performance of the cooling enclosure was modelled. The studied design configurations include use of a 3 mm copper shelve, a 3 mm VC for the RF components shelf, a 3 mm VC for both the RF components and DC shelves, and increasing the cooling air flow rate of the heat sink. The following is a summary of the main results obtained in this investigation.

i)

In the original benchmark model, one of the main problems was overheating of the 60W RF component PCB. It was found that inadequate heat removal from the electronic component caused the temperature to be 3.5 o C over the design temperature limit of the PCB material.

ii)

The initial solution was to increasing the thickness of the copper slice of the RF components from the original design of 1 mm to 3 mm. this reduced the temperature of the 60W component by 1.5 o C only, that is still 2 o C over the design temperature limit of the PCB material.

iii) A more advanced thermal management solution was contemplated by substituting the copper shelf of the RF components with a 3 mm VC. This showed that the temperature of the 60W RF component can be reduced by approximately 5.4 o C, bringing the operating temperature below the PCB temperature limit by about 2 o C.

iv)

Replacing the 15W DC component upper shelf with a VC yielded little change in the component's operating temperature (0.9 o C) which may not be cost effective.

v)

The final design was a combination of using a 3 mm thick DC upper copper shelf, a 3 mm thick VC lower shelf and increasing the cooling air flow rate of the enclosure heat sink. The operating temperature of electronic components on both shelves decreased at a constant rate by as much as 18.5 o C below the PCB's temperature limit. This however was achieved at the expense of higher fan energy consumption.

From the above results it was shown that the deployment of a VC allowed to bring the operating temperature of the 60W RF component within the acceptable PCB temperature limits. It is worth noting that in this paper the consideration of the VC was solely to investigate the technical merit of the deployment of the technology as an effective thermal management solution in electronics cooling. Hence the economic analysis was not part of the study. The high heat conduction and thermal spreading properties of a VC allows increasing the density of electronic components of different power ratings that can be mounted on a single PCB without the risk of developing hot spots or causing thermal interface between adjacent components, making RF components housing units more compact. This may present an advantage over using a large number of PCBs mounted on separate shelves and offset the high manufacturing cost associated with the VC technology.

Figure 6

 6 Figure 6 shows a side view section of the enclosure temperature. It can be seen that the highest temperature occurred at the 60W RF component. The component temperature reached 137.85 o C which is 2.85 o C above the maximum temperature limit of the PCB. The temperature of RF component 2 and 3 were approximately 82 o C which is below the specified temperature limit of 135 o C. Overall the simulation shows that the system would fail due to inadequate heat dissipation mechanism of RF component 1 and possibly the DC component of the benchmark model.

Figure 9 .

 9 It is shown that the VC reduced the temperature of the 60W RF component to 133.1 o C, which is 5.4 o C better than the benchmark model (column 2) or about 2 o C below the PCB's maximum operating temperature. The simulation results of this design however show that despite the use of VC as an effective heat spreader, heat removal from the electronics enclosure is still inadequate.

Figure 11

 11 Figure11shows the CFD simulation results of increasing cooling airflow rate for the case of an enclosure with a 3 mm solid copper RF components shelf. It shows that the operating temperature of all RF components decreased proportionally with increasing cooling airflow rate. The operating temperature of the 60W RF components dropped to 121.7 o C for flow rates of 23 m 3 /h, which is 13.3 o C below the PCB maximum operating temperature.

Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12

 3456789101112 Figure 3 DC upper shelf layout and cross section Figure 4 Lower shelf layout and cross section Figure 5 Cooling enclosure front view temperature gradient Figure 6 Cooling enclosure side view temperature gradient Figure 7 Air flow velocity distribution in the heat sink Figure 8 Pressure distribution in the heat sink Figure 9 Effect of varying shelf thickness and material Figure 10 Cross section of a vapour chamber model Figure 11 Effect of varying the heat sink air flow rate for the 3 mm copper RF components shelf Figure 12 Effect of varying the heat sink airflow rate for the 3 mm VC RF components shelf

Table 1

 1 of the cooling enclosure system specification Table2Dimension and thermal properties of the cooling system elements Table3Effect of mesh count on CFD simulation accuracy

Table 2

 2

	Element Symbol	Element	Thickness (mm)	Thermal conductivity (W/mK)
		Dielectric substrate	0.6	0.6
		Tin Solder layer	0.1	50.0
		PCB	1.4	180.0
		Thermal via circuit	1.6	22.0
		TIM	0.1	2.0
		RF copper shelf	1.0	385.0
		Aluminium Box	3.0	180.0

Acknowledgments

The authors wish to thank EPSRC (Engineering and Physical Sciences Research Council, UK) for their financial support of the project under GrantEP/P500389/1 and Themacore Europe Ltd for providing financial and technical help.

List of Figures