Design Methodology for a Rankine Microturbine ... · PDF fileJOURNAL OF MICROELECTROMECHANICAL SYSTEMS,VOL.20,NO.1,FEBRUARY2011 339 Design Methodology for a Rankine Microturbine: Thermomechanical

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 20, NO. 1, FEBRUARY 2011 339

Design Methodology for a Rankine Microturbine:Thermomechanical Analysis and Material SelectionMokhtar Liamini, Hassan Shahriar, Srikar Vengallatore, and Luc G. Fréchette, Member, IEEE, Member, ASME

Abstract—The Rankine microturbine is a microelectromechan-ical system being developed for generating mechanical and elec-trical power from waste heat, such as from automobile exhaustgases. The design of this device faces the difficult challenges of cre-ating structures rotating at high-speeds (1 000 000 r/min), sustain-ing large internal pressures (3 MPa) and temperature gradients(100 ◦C/mm), and machining millimeter-sized components of ce-ramic or metallic materials with micrometer tolerances. Here,we report an integrated approach to guide the design of theRankine microturbine by analyzing its performance and reliabil-ity. The primary performance metrics and design challenges wereidentified, and a modeling approach based on a combination oflow-order analytical models and finite-element calculations wasdeveloped for thermal and structural analyses. The results ofthese models, along with their implications for the selection ofsize, shape, and materials, are presented. The need for materialswith low thermal conductivity (10 W/m/K) for the rotor andsidewalls is highlighted, along with the expected levels of stressesand deformation and their impact on reliability. Viable device con-figurations and materials (silica, zirconia, and titanium alloys) areproposed for operation at elevated temperatures. The approach tothe modeling used in this paper is expected to be of value for thepreliminary design of other microsystems subjected to stringentmechanical and thermal loading. [2010-0125]

Index Terms—Energy harvesting, materials selection, micro-pump, PowerMEMS, Rankine microturbine, thermomechanicalanalysis.

I. INTRODUCTION

THE RANKINE microturbine is a microelectromechanicalsystem (MEMS) being developed for waste-heat recovery,

such as from automobile exhaust gases [1]. This power-planton-a-chip uses waste heat to generate high-temperature steam,which then drives a turbine to produce useful mechanical orelectrical power. This device is part of a family of MEMSfor power generation and energy conversion based on micro-rotating machinery [2], [3]. Depending upon the application,

Manuscript received April 30, 2010; revised August 18, 2010; acceptedOctober 4, 2010. Date of publication December 20, 2010; date of currentversion February 2, 2011. This work was supported in part by General Motorsof Canada, Inc., and in part by the Natural Sciences and Engineering ResearchCouncil of Canada. Subject Editor S. M. Spearing.

M. Liamini and L. G. Fréchette are with the Départment de GénieMécanique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada(e-mail: [email protected]; [email protected]).

H. Shahriar was with the Department of Mechanical Engineering, McGillUniversity, Montreal, QC H3A 2K6, Canada. He is now with ENERCONCanada Inc., Montreal, QC H3B 4W5, Canada (e-mail:[email protected]).

S. Vengallatore is with the Department of Mechanical Engineering, McGillUniversity, Montreal, QC H3A 2K6, Canada (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2010.2093565

Fig. 1. Schematic cross section of a Rankine microturbine: (1) Rotor.(2) Thrust bearing. (3) Journal bearing. (4) Evaporator. (5) Condenser.(6) Insulating sidewall. (7) Pump. (8) Generator. (9) Seal. The diameter andthickness of the rotor are 4 mm and 400 μm, respectively. The arrows showthe various flow paths: Red shows the path taken by the steam as it enters theturbine and goes through the journal bearing and thrust bearing; orange showsthe path of the steam through the thrust bearing; and blue shows the path takenby the liquid through the pump.

the Rankine microturbine could generate between 0.1 and30 W for a device volume of less than 1 cm3. It could power theoperation of networks of actuators and sensors [4] by absorbingsolar radiation or scavenging waste heat from ambient sources.Alternatively, the devices could be packed together in largenumbers in a modular approach for distributed power genera-tion. For example, a set of Rankine microturbines could provideelectric power in the range of 0.5–2 kW onboard automobilesby harvesting waste heat from the exhaust.

The first attempt to develop MEMS-based engines operatingon the Rankine vapor power thermodynamic cycle commencedin 2002 [5]. A schematic cross section of this device, which is∼1 cm in diameter and ∼2 mm in thickness, is shown in Fig. 1.The rotor (1) is held in place using fluid-film thrust bearings(2) and a journal bearing (3). The evaporator (4), which isused to generate high-temperature steam, is separated from thecondenser (5) by a cylindrical sidewall (6), which functions asa static insulator. The pump (7) is located underneath the rotor,and a generator (8) is integrated into the stationary and rotatingstructures to generate electricity. The steam that exits from theturbine is condensed into liquid water and then pumped backinto the evaporator in a closed cycle.

The first demonstration of the core microturbopump for theRankine microturbine was reported in 2006 [6]. That deviceconsisted of a five-layer stack (with four silicon wafers andone glass wafer) and was operated at room temperature with airto characterize the rotating components, including the turbine,pump, seal, journal bearing, and thrust bearing. A maximumspeed of 330 000 r/min was achieved with a microfabricated

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340 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 20, NO. 1, FEBRUARY 2011

Fig. 2. Schematic illustration of the multispool configuration of four Rankinemicroturbines for an estimated power output of 25 W [7].

silicon rotor that had a diameter of 4 mm and operated onair bearings. The inward viscous pump, which was tested tospeeds of 120 000 r/min, could pressurize to 240 kPa anddeliver a maximum flow rate of 9 mg/s. These encouragingresults motivate us to develop the next generation of Rankinemicroturbines using water and steam as the working fluids,which imply operation at higher temperatures of a few hundreddegrees centigrade. We envision a multispool configurationconsisting of four Rankine microturbines arranged in series, asshown in Fig. 2. The first three spools (denoted as Turbines 1,2, and 3) are used for electric power generation. Turbine 4 isexposed to lower temperature steam and drives the pump. Thetotal electric power produced by this configuration is estimatedto be ∼25 W, assuming that the turbines driving the generatorsrotate at 1 200 000 r/min and that the turbine driving the pumprotates at 600 000 r/min [7]. Such rotational speeds have beendemonstrated to date with silicon microturbines but with room-temperature gases [8].

Implementing the Rankine thermodynamic cycle usingminiaturized devices requires operating at high temperatures(200 ◦C–700 ◦C) and high pressures (0.3–3 MPa) in asteam environment, sustaining large temperature gradients(100 ◦C/mm), and turbomachinery rotating at speeds as largeas 1 000 000 r/min [1], [5]. These challenges are not com-monly encountered in the structural design of other types ofmicrosystems and microengines [3], [9]. Because the designspace for Rankine microturbines is still largely uncharted, weseek, in this paper, to develop robust and efficient methodolo-gies to identify designs that can enable the development ofdevices with excellent performance and sufficient reliability. Acomparison of the four turbines in Fig. 2 reveals that Turbine4 embodies within itself all the major design challenges interms of high-speed rotating components, fluid management,thermal insulation, and structural integrity. This device maybe characterized as a miniaturized pressure vessel that con-tains high-speed rotating components and has to sustain largetemperature gradients. Fig. 3 shows a schematic cross sectionof the static (nonrotating) component, which consists of twocircular plates and the cylindrical sidewall. The upper and lowerplates are maintained at different temperatures during operationbecause they are in contact with the (hot) evaporator and (cold)condenser, respectively.

Fig. 3. Schematic cross section of the static structure consisting of the upperand lower plates and a cylindrical sidewall. The curved arrow represents heatleakage through the side wall, P is the internal pressure, ro is the outer radiusof the sidewall, t is the wall thickness, and L is the wall height.

The remaining sections of this paper focus on the structuraldesign of Turbine 4 and are organized as follows. Section IIoutlines the primary performance goals and design challengesfor this device. Section III discusses the preliminary selection ofmaterials for the various components, resulting in a qualitativetradeoff between performance, reliability, and manufacturabil-ity. This selection is refined by undertaking detailed thermalanalysis of the performance and mechanical analysis of relia-bility; these models and the results are presented in Sections IVand V, respectively.

II. PERFORMANCE METRICS AND DESIGN CHALLENGES

The areal power density (i.e., power output per unit devicearea) is the primary metric for the performance of the Rankinemicroturbine, as it relates the power provided to the manufac-turing cost. The power output can be increased by increasingthe temperature difference between the inlet and outlet of theturbine or, equivalently, between the evaporator and condenser.For automotive applications, this difference ranges from 150 Kto 700 K; the lower end is the value that is generally recog-nized as the minimum useful temperature difference for theRankine cycle, and the upper bound corresponds to the max-imum difference between the temperature of exhaust gasesand the ambient. In addition, the power can be maximizedby increasing the pressure ratio of the pump; our previousstudies indicated that pressures of ∼3 MPa are sufficient togenerate power at the desired level of 1–25 W. Finally, thepower output per unit device area can be increased by efficientminiaturization; for turbomachinery, this is achieved at hightangential tip speeds by spinning the rotors between 500 000and 1 000 000 r/min for rotors with a diameter of 4 mm.

These performance goals are limited by the operating con-ditions (evaporator and condenser temperatures and internalpressure), available fabrication techniques, and reliability is-sues. The device can experience unwanted heat leakage (dueto temperature gradients in excess of 100 ◦C/mm), mechanicaland thermomechanical stresses (due to rotation, fluid pressure,and differential thermal expansion), and unwanted boiling orcondensation of the working fluid. This last mentioned issuearises because efficient operation of the device requires theworking fluid (H2O) to be in the vapor phase in the turbine,bearings, and seals, but in the liquid phase in the pump.In addition, deformation due to thermal expansion and fluidpressure can lead to distortion of the structure; in turn, thiscan lead to undesirable changes of critical gaps, such as thoseof the seals and thrust bearings. The parameters that permit

LIAMINI et al.: DESIGN METHODOLOGY FOR A RANKINE MICROTURBINE 341

TABLE ITHERMAL CONDUCTIVITY k (IN WATTS PER METER PER DEGREE KELVIN) OF SELECTED OXIDES, CERAMICS, AND ALLOYS.a

us to address these challenges are the component geometry,layout, and choice of materials used for the device. In thenext section, we consider the preliminary selection of materialsand identify tradeoffs between performance, reliability, andmanufacturability.

III. PRELIMINARY SELECTION OF MATERIALS

The materials used for the components of the Rankine mi-croturbine must lead to high performance, ensure sufficientreliability, and be compatible with the limitations imposed bystate-of-the-art microfabrication techniques. To begin with, aset of materials that can maximize performance is identifiedfollowing a standard approach [10], [11]; subsequently, thisselection is refined by taking reliability and manufacturabilityinto account.

A. Selection for Performance

The performance of the Rankine microturbine can be en-hanced by increasing the temperature difference between theevaporator and condenser to maximize the power output andefficiency of the cycle. As a corollary, any heat transfer by con-duction through the solid components (cylindrical sidewalls androtor) will degrade the performance of the device. Therefore,structural materials with low values of thermal conductivity(k) must be selected for the cylindrical sidewalls and rotor.An extensive survey of the thermal conductivity of structuralmaterials showed that oxides (zirconia, silica, Pyrex glass,titania, and quartz) exhibit the lowest values in the range of1 to 10 W/m/K over a wide range of temperature (Table I).Polymers and elastomers were excluded from considerationbecause their service temperatures are lower than the operatingtemperature of the device [10]. The thermal conductivities of

metals and alloys are typically higher by one or two orders ofmagnitude, but certain titanium and nickel-based alloys haverelatively low thermal conductivities of ∼10 W/m/K. Alsolisted in Table I are the structural ceramics (Si, SiC) used inthe current generation of microengines [3], [6]; these materialshave much higher thermal conductivities ranging from 50 to270 W/m/K. Therefore, from a performance viewpoint, thepreferred materials for the cylindrical sidewall and rotor aresilica, zirconia, titania, Pyrex, quartz, and Ti-alloys.

B. Selection for Reliability

The cylindrical sidewall and rotor must be designed towithstand the stresses due to fluidic pressure and differentialthermal expansion. In addition, the rotor is subjected to stressesarising from rotation during operation. Under these stresses,the oxides and ceramics are susceptible to failure by brittlefracture, and the alloys are susceptible to failure by yielding andductile fracture. In addition, creep during operation at elevatedtemperatures is also a concern [3]. A simple estimate for theorder of magnitude of stresses due to fluidic pressure can beobtained by considering the hoop stress σhoop = (Pro/t) inthe cylindrical sidewall, as shown in Fig. 3. Thus, for ro =2 mm and P = 3 MPa, the hoop stress is ∼60 MPa for awall thickness of 100 μm. Accounting for stress concentrationat the edges, the tensile stress within the structure can beconservatively estimated at ∼100 MPa.

The brittle strengths of micromachined silicon and siliconcarbide have been reported to be as high as a few gigapas-cals [20]. The corresponding values for silica and zirconiaare lower, with nominal fracture strengths of ∼100 MPa [10]and ∼350 MPa [21], respectively. These values, however, areextremely sensitive to surface flaws and can decrease by anorder of magnitude, depending on the details of the processing


parameters used during microfabrication [22], [23]. In contrast,the yield strengths of Ti alloys maintain high values of severalhundred megapascals over the temperature range of interest forthe Rankine microturbine [10]. Therefore, these ductile alloysoffer significantly higher reliability than the oxides or ceramics.

C. Selection for Manufacturability

Experience with the first generation of the Rankine microtur-bine provides some guidelines for the geometric requirementsimposed on microfabrication: 1) ability to etch features todepths of 300 to 400 μm, depth-to-width aspect ratios of up to5 : 1, low surface roughness, vertical sidewalls, and machiningtolerances of ∼1 μm, and 2) ability to achieve high-strengthbonding to create pressurized 3-D flow channels. Ideally, allthese challenging requirements must be met by processesthat enable batch fabrication of components and systems. Atpresent, this is possible only for single-crystal silicon usinga combination of deep reactive-ion etching (DRIE) and waferbonding [3], [24].

For other materials, methods for anisotropic bulk microma-chining to produce vertical sidewalls and large aspect ratios arein relatively early stages of development. Recipes have beendeveloped to etch titanium [25], silicon oxide [26], and Pyrexglass [27] to depths of 100–400 μm at rates of∼1 μm/min usinginductively coupled plasma. In addition, several machining-based processes, including laser micromachining, high-speedmilling, electrodischarge machining, and electrochemical ma-chining, are being developed. However, these techniques donot yet achieve the desired combination of etch depths, sur-face finish, and tolerance or simply lack maturity at present.Therefore, significant process development will be required ifsilica, zirconia, quartz, or titanium alloys are to be used for thecomponents of the Rankine microturbine.

D. Summary of Material Selection

For the purpose of material selection, the components ofthe Rankine microturbine can be split into two groups. Thefirst group consists of the evaporator, the condenser, the pump,and the layers containing the stator blades. All these compo-nents contain features that require vertical etching to depths of50–300 μm with micrometer tolerance but are not subjected tosignificant stresses during operation. The thermal resistance ofthese components has no significant impact on device perfor-mance. Therefore, the primary consideration for material se-lection is based on manufacturability, and single-crystal siliconprocessed using a combination of DRIE and wafer bonding iscurrently the material of choice for these components.

The second group consists of the cylindrical sidewalls androtor. The analysis of material selection for these componentscan be summarized in terms of a qualitative tradeoff betweenperformance, reliability, and manufacturability. Thus, silica andzirconia offer excellent performance, poor reliability, and mod-erate manufacturability; titanium alloys offer moderate perfor-mance, excellent reliability, and relatively poor machinability;and single-crystal silicon offers poor performance, moderatereliability, and excellent manufacturability. To further refine

this selection, we undertake thermal and mechanical analysesto quantify the effects of material properties and size on perfor-mance and reliability, as discussed in the following sections.

IV. THERMAL ANALYSIS OF PERFORMANCE

The primary objective of the thermal analysis is to establisha link between device performance (in terms of thermal effi-ciency) and the structural details (materials, shape, and size) ofthe cylindrical sidewalls and rotor. The analysis of the former isstraightforward because the structure is simple, and conductionis the dominant source of heat loss. In contrast, the analysisof the rotor is considerably more complicated because this isa specific instance of the more general problem of computingheat transfer in a solid structure that is surrounded by multipleheat paths. This problem can be addressed using the methodof finite elements to compute heat transfer in the structural andfluid regions; however, this technique is not well suited for arapid exploration of the design space because each change inconfiguration requires costly remeshing and reanalysis. Instead,we propose an approach that links a finite-element model of therotor with lumped models for the surrounding components tocombine the accuracy of discretized numerical modeling withthe flexibility of low-order models. These details are presentedin the following sections.

A. Thermal Analysis of Cylindrical Sidewall

The first step in the analysis of the sidewalls shown in Fig. 3is to express the thermal efficiency η of the device as a functionof heat loss; thus

η=welectric

qevaporator + qstructure_loss=

welectric

qevaporator + (ΔT/Rth).

(1)

Here, welectric is the electric output power, qevaporator isthe heat provided to the evaporator, and qstructure_loss is theheat loss through the sidewalls, which is a function of thetemperature difference ΔT and the axial thermal resistance ofthe wall Rth = L/kA, with A as the wall cross-sectional areain the direction of heat flow.

To obtain the heat given to the evaporator (qevaporator)and the electric power (welectric), the thermodynamic Rankinecycle was calculated for component efficiencies typical of theRankine microturbine device by specifying the hot and coldsource temperatures as boundary conditions; the details of thesecalculations are presented in [28]. For a representative exampleof energy harvesting from an automotive engine, the hot tem-perature was specified as 800 K and the cold temperature as293 K, leading to qevaporator = 78 W and welectric = 8.4 W fora flow rate of 24 mg/s of water.

Using these values, (1) can be used to explore the effectsof geometry and materials on efficiency, and a representativeexample is shown in Fig. 4.

If silica or zirconia (thermal conductivity of ∼2 W/m/K) areused, then the sidewalls can be relatively thick (∼500 μm) andstill achieve an efficiency near the asymptotic value of 10.7%with no heat loss. Ti-alloys (∼10 W/m/K) are also a viable


Fig. 4. Effect of thermal conductivity and sidewall thickness on the efficiencyof the Rankine Microturbine. These curves were computed for a device withwall radius and height of 2 mm and 0.5 mm, respectively, and a temperaturedifference of 500 K between the evaporator and condenser. Colored bandsrepresent materials and their thermal conductivities over a temperature rangefrom 298 K to 773 K.

Fig. 5. Schematic cross section showing the dimensions used for thermalanalysis of the rotor. The fluidic components surrounding the rotor are rep-resented by an inlet radius rin, an outlet radius rout, and a radial or axial gap,as shown here for the generator. The dimensions of the radii and gaps for thevarious components are listed in Table II.

option, although the wall thickness must be less than 200 μmto achieve the same efficiency. However, using either Si or SiCwill incur a severe penalty in terms of a precipitous drop indevice efficiency due to high heat loss.

B. Thermal Analysis of the Rotor

The thermal analysis of the rotor is more challenging becausethis structure is surrounded by multiple fluidic components,each leading to heat transfer to the surrounding structure orflow. Therefore, the first step is to identify the different heat-transfer paths that are pertinent to the device. There is no pathfor conduction because the rotor is solely supported by fluidicbearings and is not in contact with any solid component, andradiation was found to be negligible compared with convectiveheat transfer. Therefore, the convective heat transfer from therotor to the surrounding fluids is the dominant source of theheat transfer considered here. The rotor is modeled as a simpledisk with a diameter of 4 mm and thickness of 400 μm, and thewidth of the static structure is fixed here to 100 μm (Fig. 5).

TABLE IIDIMENSIONS OF THE RADII AND GAPS OF THE FLUIDIC COMPONENTS

USED FOR THERMAL ANALYSES

Fig. 6. Schematic illustration of the coupled heat-transfer modeling approachconsisting of discretized finite-element model for the rotor surrounded bylumped models of the adjacent components. The temperature contours arefor the representative case of a Pyrex rotor (with a thermal conductivity of1.4 W/m/K), as discussed later in this section.

Since the problem is axisymmetric, a cross section of the rotorin the radial–axial plane is considered. The geometries of thefluidic components surrounding the rotor are represented byan inlet radius rin, outlet radius, rout, and the gap betweenthe surface of the rotor and the adjacent static surface. Thevalues of the radii and gaps for each component are listed inTable II. The calculations were performed assuming that steamenters the turbine at 800 K and that the liquid enters the pumpat 293 K.

Our approach for computing the heat transfer through therotor is to combine a 2-D axisymmetric finite-element model ofthe rotor with various lumped-parameter models for convectiveheat transfer in the fluidic components, as shown schematicallyin Fig. 6.

Each component is represented either as a black box thatrelates the heat transfer through the component to the temper-ature difference between the rotor surface and external flow orstatic wall temperatures or simplified to a thermal resistanceRth = (ΔT/q), whenever possible. The derivation of the vari-ous lumped models is briefly summarized next, beginning withthe models for convective heat transfer.

Assuming 2-D axisymmetric incompressible flow with con-stant properties, the equations for conservation of mass andmomentum can be simplified to obtain the velocity profiles[29]. Subsequently, the velocity profiles can be introduced


in the equations for energy conservation given in cylindricalcoordinates r, θ, and z to obtain [29]

ρcp

(vr

∂T

∂r

)= kf

(1r

∂

∂r

(r∂T

∂r

)+

∂2T

∂z2

)+ μΦ (2)

μΦ = μ

[(∂vr

∂z

)2

+(

∂vθ

∂z

)2

+(

∂vθ

∂r− vθ

r

)2

+ 2

{(∂vr

∂r

)2

+v2

r

r2

}]. (3)

Here, ρ is the density, cp is the specific-heat capacity atconstant pressure, kf is the fluid thermal conductivity, μ is thedynamic viscosity, and T is the temperature. These equationscan be solved with the ultimate goal of obtaining a relationshipbetween the heat flux in each component and the correspondingboundary temperatures. This is achieved by first obtaining theflow velocity profile and then the temperature profile. Severaldifferent cases can be identified, as described next.

1) Boundary Layer Heat Transfer in External DevelopingFlow on Plates: On certain surfaces, the Reynolds numbersare sufficiently high that the boundary layer is relativelythin compared with the passage height. For example, theReynolds number ranges from 100 to 2000 in the turbine-blade passages, and the flow is expected to be laminar withrelatively thin boundary layers. The flow can be representedas external flow over a plate with the free stream temper-ature given by the core flow. The conservation equationscan be simplified by assuming dominant radial flow parallelto the surface (vr � vθ, vz) and dominant normal gradients((∂vr/∂z) � (∂vr/∂r), (∂vθ/∂z), (∂vθ/∂r)) for the veloc-ity boundary layer, and (∂T/∂z) � (∂T/∂r) for the thermalboundary layer. With these assumptions, (2) and (3) can besimplified to give

vr∂T

∂r=

k

ρcp

∂2T

∂z2+

μ

ρcp

(∂vr

∂z

)2

. (4)

The ideal method for determining the convective heat transferin the boundary layer is to solve this equation and then obtainthe heat flux in each zone q′′i using Fourier’s law evaluated atthe surface

q′′i = −kf∂T

∂z

∣∣∣∣z=zsurface,i

. (5)

This approach, however, is feasible only for a few simplecases, such as laminar flow, where a similarity solution canbe used. In most practical cases, the convection coefficienth is given by empirical correlations expressed in terms ofnondimensional Reynolds number (Re) and Prandtl number(Pr). If empirical correlations are not available, then numericalsimulations or experiments are needed to obtain the convectioncoefficient. The convective heat transfer can then be expressedas a thermal resistance Rth = 1/(hA), where A is the surfacearea exposed to the flow.

The blade surfaces are modeled here using boundary-layertheory by assuming steady, incompressible, laminar flow, uni-

form surface temperature, and no pressure gradient along theblade. These simplifications lead to an analytical expression forthe thermal resistance in the bladed zone given by [30]

Rth =c

0.664kf ARe Pr1/3. (6)

Here, c is the blade chord, and A is the wetted blade surfacearea. Comparison between conduction in the blades and con-vection at the blade surface shows the former to be dominant.Hence, the blades were assumed to be isothermal. Similarly, thethermal resistance of the flat surfaces between the blade rows isgiven by

Rth =(rin−rout)

√μ/ρ

C k A

(ln

rout

rin

)−1

, C =m

2π ρλ. (7)

Here, λ is the height of the blade passage, m is the massflow rate, rin is the internal radius, and rout is the externalradius of the annulus bounded by two adjacent blade rows. Thisexpression accounts for changes in the section passage fromstage to stage.

The centers of the turbine and pump can be modeled usinga correlation found in the literature on flows over rotatingdisks, which provides the convection coefficient for laminarand incompressible flow as a tabulated function of the Prandtlnumber [31]. The thermal resistance in the turbine and pumpcenters is given by

Rth =1

hA=

√μ

ρω

1kfA f(Pr)′

(8)

where ω is the rotating velocity.2) Heat Transfer Through a Fluid Layer Between Two Sur-

faces: A 2-D Simplification: At lower Reynolds numbers, theboundary layers rapidly span the entire gap or channel height,so the heat transfer now occurs between the two adjacentsurfaces across the fluid film. In this case, the fluid film canbe represented as a simple thermal resistance; however, a morecomplex model is required if viscous dissipation or advectionare significant.

a) Simple case: Conduction through the fluid film: If theNusselt number approaches unity, the heat transfer in a fluidfilm between two surfaces is driven mainly by conduction.This is the case for the journal bearing. After simplifying themomentum equations to obtain the velocity profile, nondimen-sioning the energy equation, and studying the scale order of thevarious nondimensional terms obtained, it was found that themain physical phenomenon is radial conduction across the fluidfilm. The heat transfer can then simply be modeled using a 1-Dthermal resistance.

b) Viscous dissipation with dominant circumferentialflow: For a structure in motion, viscous dissipation (governedby the Eckert number) can become significant. This implies thatthe simple approach of using a thermal resistance is no longervalid because the fluid acts as a heat source, and the temperatureis a nonlinear function of the gap. Therefore, the rate of heattransfer was determined by first finding the velocity profilesusing a simplified version of the momentum equations andthen using the velocity profile in the energy equation to obtain


an expression for the temperature profile and heat flux at thesurface of the rotor. This approach was used to model the thrustbearings, generator gap, and seals. The governing equationsare based on momentum and energy conservation, with theassumption of stable, incompressible, laminar, and developedflows. The dominant flow is the circumferential component,which can be expressed as

vθ = ωrz

τ. (9)

Here, r is the radial axis, z is the axis of rotation, and τ isthe thickness of the fluid film. Introducing this expression in(4) and eliminating terms that are negligible, we obtain

∂2T

∂z2= − μ

kf

ω2r2

τ2. (10)

This equation is then solved analytically to give the temper-ature profile as

T (r, z) = − μ

kf

ω2r2z2

2τ2+

(μω2r2

kfτ− q2

kf

)z + T1. (11)

In this expression, T1 is the temperature at the (lower) staticsurface, and q2 is the heat flux rate at the (upper) rotor surface.

c) Viscous dissipation and radial advection: If thePrandtl number is high, which is the case for water, the flowmay not be thermally developed even if the viscous flow is fullydeveloped. This will lead to higher temperature gradients in thefluid and, hence, to increased rates of heat transfer. The flowand temperature profiles can be solved using computationalfluid dynamics, but simplified solutions are also possible whenthe flow is fully developed. For example, the flow in thepump is fully developed and can be represented as a Poiseuilleradial flow between two disks. Simplification of the momentumequation leads to an expression for the radial velocity profile

vr =−3m

πτ3ρrz(z − τ). (12)

Introducing this expression into (4), and simplifying usingorder-of-magnitude analysis, we obtain

ρcpvr∂T

∂r= kf

∂2T

∂z2+ μ

ω2r2

τ2. (13)

This partial differential equation can be solved numericallyto obtain the temperature profile with respect to the speci-fied boundary conditions. Again, the heat flux at a surfaceis obtained by taking the spatial derivative of the calculatedtemperature normal to the surface.

3) Rotor Conduction With Lumped Models as BoundaryConditions: The rotor of the Rankine microturbine is sur-rounded by fluid on all sides, as shown in Fig. 6. The identity ofthe dominant path of heat transfer is not clear, which makesit difficult to model heat transfer using a thermal resistance.Instead, the finite-element method (FEM) was used to analyzeheat transfer within the bulk of the rotor. A commercial multi-purpose solver (COMSOL) was used for this analysis, andmesh analysis indicated that 5000 linear triangular elementswere sufficient to ensure convergence. The meshed domain was

Fig. 7. Thermal modeling methodology combining finite-element calculationof the 2-D temperature field in the rotor with lumped models of the surroundingcomponents.

coupled toMATLAB functions representing the various lumpedmodels (defined earlier) for the fluidic components surroundingthe rotor through the surface temperatures and heat fluxes. Theprocess is shown in Fig. 7. Initial temperatures were imposedat the boundaries of the rotor in the FEM model, enablingthe solution of the 2-D temperature profile in the structure.The heat-transfer rates were extracted in each zone and werethen imposed as boundary conditions in the lumped models attheir interface with the rotor. The lumped models were solvedindividually to obtain the mean surface temperature at the rotorin each zone. The temperature boundary conditions in the FEMmodel are then updated with these temperature values, and theprocess is iterated until the temperatures and heat-transfer ratesconverge.

4) Results: The models described earlier were used to con-duct parametric studies to understand the effects of the thermalconductivity of the rotor on the efficiency of the Rankinemicroturbine and on the maximum pump temperature, and theresults are shown Fig. 8.

The thermal conductivity of the rotor was varied between 1and 15 W/m/K, which covers the properties of silica, zirco-nia, and titanium alloys. Over this range, the device operateswith sufficiently high efficiency and low pump temperatures.However, as the thermal conductivity increases, the maximumpump temperature increases significantly with respect to theboiling temperature of the working fluid, which is undesirableduring operation. Maintaining the thermal conductivity below3.2 W/m/K using silica and zirconia can limit the temperaturein the pump to ∼310 K and provide relatively high efficienciesof ∼10%. Ti alloys with conductivity of up to 10 W/m/K arealso found to be acceptable, although with less margin of safetybefore boiling in the pump.


Fig. 8. Effect of the rotor thermal conductivity on the thermal efficiency andthe maximum pump temperature (for pump inlet temperature of 293 K). Thediameter and thickness of the rotor are 4 mm and 400 μm, respectively.

This study also helped to identify the main thermal paths inthe device. For the configuration that was studied, the principalpath for heat flux on the top surface are the blade rows with athermal resistance in the range of 25–50 K/W, and the principalpath on the bottom surface is the pump with a thermal resistanceof∼2 K/W. This leads to a relatively long conduction path fromthe hot zone near the blades to a cold zone near the pump. Thiscan be seen in Fig. 6, which shows the temperature contoursobtained for a Pyrex rotor with k = 1.4 W/m/K. An alternatedesign of interest is one in which the center region on the topsurface of the rotor is occupied by a top thrust bearing witha small gap of about 1.5 μm. The thermal resistance of sucha region is very low (∼5 K/W) compared with the thermalresistance of the blade rows. This implies that the main thermalpath in the rotor would be close to the central axis, reducingthe effective conduction length and the resulting thermal re-sistance of the rotor. Using materials with the lowest thermalconductivity, such as the oxides, then becomes mandatory.The device configuration and layout of the components aroundthe rotor can therefore affect heat loss through the rotor andhave a significant effect on the thermal efficiency and materialselection.

C. Summary of Thermal Analysis

Heat transfer in the cylindrical sidewalls can be analyzedusing a simple 1-D model, but a more complicated approachwas required to analyze the rotor. The essential elements of thisapproach are the following: 1) to define the boundary condi-tions based on the desired operating temperatures; 2) to selectrepresentative ranges of values for the other device param-eters, such as flow rates, rotation speed, efficiencies of pumpand turbine, and dimensions; 3) to identify the most probableheat-transfer mechanisms (conduction, convection, radiation)and paths; 4) to represent the heat transfer quantitatively usingsimple analytical models and empirical correlations or by usingnumerical techniques such as the finite-element analysis andcomputational fluid dynamics if required; and 5) to coupletogether the models for the various heat-transfer paths, along

with the appropriate boundary conditions, to evaluate heattransfer through the device and its temperature distributions.

A major result of the thermal analysis is the need for materi-als with thermal conductivity that is less than 10 W/m/K for thesidewalls and the rotor to minimize the impact of heat losseson the device efficiency. Therefore, the materials of choiceare the oxides (zirconia, silica, Pyrex, and quartz) followedby titanium alloys. Although single-crystal silicon is widelyused in MEMS, it can be discarded as a possible choice herebecause this material leads to unacceptably low efficiencies;interestingly, the same conclusion was reached in a previousstudy of the effects of miniaturization on the performance ofregenerative heat engines [32].

V. MECHANICAL ANALYSIS OF RELIABILITY

In this section, we analyze the effects of materials, geome-tries, and packaging strategies on the reliability of the staticstructure and rotor of the Rankine microturbine. The devicecan fail if stresses exceed the brittle strength or yield strength.Alternatively, significantly large deformations of some compo-nents can change the dimensions of the air bearings, resultingin failure due to unstable operation.

A. Mechanical Analysis of the Static Structure

The stresses and deformations in the static structure shownin Fig. 3 were analyzed using the method of finite elements.The details of the pumps and microfluidic channels in the evap-orator and condenser were omitted from the analysis, and bothcomponents were modeled as flat plates of single-crystal silicon(Fig. 9). Parametric studies were conducted using COMSOL toanalyze the effects of the sidewall material, sidewall thickness,temperature of the evaporator, and internal pressure on thestresses and deformations.

The model was meshed using 2-D Lagrangian elements oftriangular shape, and the mesh was refined at the internal corneredges. Fillets of 2-μm radius were incorporated at these corneredges in order to ensure convergence of solutions. First, themechanical stresses generated due to an internal pressure of1 MPa were studied as a function of sidewall thickness andmaterial. Sidewalls with thickness of less than 100 μm resultedin edge stresses greater than 100 MPa [Fig. 10(a)]. A simpledesign strategy for reducing these stresses is to increase thefillet radius; thus, increasing the radius from 2 to 30 μm resultedin a reduction of stresses by a factor of three. Further, themagnitudes of the maximum tensile stresses, which occur atthe internal corners, were found to be only a weak function ofthe sidewall material.

In contrast, the thermal stresses within the structure arestrong functions of the material properties of the sidewall, evap-orator, and condenser. Even if the static structure is subjectedto a uniform temperature, thermal stresses are generated dueto differences in the coefficients of thermal expansion (CTEs)of the sidewalls with respect to the top and bottom layers[Fig. 10(b)]. If the sidewall has a higher CTE than the othertwo layers, then this structure will bulge radially outwards,thereby creating thermal strains which lead to edge stresses.


Fig. 9. (a) Axisymmetric schematic of the finite-element model showing the internal pressure P , evaporator temperature Th, sidewall thickness t, and sidewallmaterial M . The sidewall is bonded to the evaporator and condenser; however, the details of the plumbing in the latter structures are ignored in this analysis.(b) The fixed parameters of the model include the internal radius ri, condenser temperature Tc, and single-crystal silicon as the material for the evaporator andcondenser. The model incorporates lateral constraints along the axis of symmetry.

Fig. 10. Deformed structure and stress contours for the simplified static structure under different loading conditions: (a) Internal pressure of 1 MPa with siliconwalls; the edges at the intersections of the sidewall with the top and bottom layers are the regions of stress concentration. (b) Uniform temperature field of 500 Kand a sidewall CTE of 10.5 × 10−6/K. (c) Temperature difference ΔT of 200 K; the top layer expands relative to the bottom layer, generating stresses at thebottom edge.

The magnitude of these stresses reduces with increasing wallthickness.

Next, the effects of temperature gradient were studied bysetting the evaporator at a higher temperature than the con-denser [Fig. 10(c)]. This temperature difference causes the topplate to expand radially outward compared with the bottomplate. In addition to this effect, sidewalls with higher CTEsundergo greater expansion at the top portion compared with thebottom, since they sustain an axial temperature gradient. Thesuperposition of these two thermal-expansion effects generatesthermal stresses on the order of hundreds of megapascals,which are significantly larger than the stresses caused by in-ternal pressures.

In analyzing the deflections, however, the coupled effects ofinternal pressure and temperature difference were considered.A graph of the axial and radial deflection as a function of theCTE of the sidewall is shown in Fig. 11. As the CTE of thesidewall increases, the radial deflection increases, as expected,but the axial deflection decreases monotonically. This non-intuitive behavior is due to the increase in the counterclockwisemoment applied at the edges of the top plate by the sidewall,which reduces the axial deflection at the center of the plate.The magnitudes of the deflections, which range from 0.75to 1.75 μm, are comparable with the operating gaps for thethrust bearings, seals, and pump. Therefore, deflections of thismagnitude can lead to unreliable operation of the device.

The stresses in the structure are minimized when the CTEsof the wall and the plates are equal. This condition, however,may not minimize the axial and radial deflections. The optimalvalue for the CTE of the wall for reducing deflection dependson the applied loads and wall geometry. Hence, the selection of

Fig. 11. Maximum axial and radial deflections of the static structure as afunction of the CTE of the wall material. An internal pressure of 1 MPaand a temperature difference of 200 K between the evaporator and condenserare applied. The thickness of the sidewall is 100 μm. The evaporator andcondenser are modeled as flat plates of a single-crystal silicon with a CTE of3.5 × 10−6/K.

the wall material leads to a tradeoff between reducing stressesand deflections.

The full set of parametric numerical studies was used toformulate empirical scaling relationships for the stresses anddeformations as functions of the operating conditions (pressureP and temperature difference ΔT between the evaporator andcondenser) and properties of the sidewall (Young’s modulus E,CTE, α, and thickness t). It was observed that the stress due to


TABLE IIIRESULTS FROM THE FINITE-ELEMENT ANALYSIS ILLUSTRATING THE EFFECTS OF SIDEWALL PARAMETERS ON THE MAXIMUM

TENSILE STRESSES AND MAXIMUM AXIAL DISPLACEMENTS IN THE STATIC STRUCTURE. IN ALL CASES, A FILLET

WITH A RADIUS OF 30 μm WAS INCORPORATED INTO THE FINITE-ELEMENT MODEL

TABLE IVRESULTS FROM THE FINITE-ELEMENT ANALYSIS ILLUSTRATING THE EFFECTS OF SIDEWALL MATERIALS ON THE MAXIMUM TENSILE

STRESSES AND MAXIMUM AXIAL DISPLACEMENTS IN THE STATIC STRUCTURE. IN ALL CASES, THE FINITE-ELEMENT MODEL

INCORPORATES A SIDEWALL WITH A THICKNESS OF 100 μm AND A FILLET WITH A RADIUS OF 30 μm

the internal pressure scales as P (Ea/tb) with 0 < a < b < 2and the thermal-stress scales as ΔT (α Ec td), where both cand d take values between zero and one. Thus, increasing thewall thickness reduces the stress due to internal pressure, butincreases the thermal stresses. Quantitative results for represen-tative designs and operating conditions are listed in Table III.The baseline structure has a sidewall with a thickness of100 μm, Young’s modulus of 140 GPa, and CTE of 3.5 ×10−6/K; fillets with a radius of 30 μm are incorporated at theintersections of the sidewall with the plates. Subsequently, eachdesign parameter was varied in turn over a range covering theproperties of silica and titanium alloys, and the stresses anddeformations in the static structure were analyzed. In this table,σP,max is the maximum tensile stress due to an internal pressureof 1 MPa, and σT,max is the maximum tensile stress due toa temperature difference of 200 K across the sidewall. Thecorresponding axial center deflections are denoted as δP,max

and δT,max, respectively.The numerical analyses of the mechanical reliability of

the static structure can be summarized as follows. First, fortypical operating conditions, the temperature gradient acrossthe sidewall has a greater impact on the stresses comparedwith the internal pressure within the structure. Second, as thethickness of the sidewall increases, the pressure-induced tensilestresses decrease, but the thermal stresses increase. However,a sidewall with a thickness of 100 μm is sufficient to limitboth these stresses below the critical values for silica, zirconia,and titanium alloys (Table IV) but with low margins of safetyfor brittle fracture of the oxides. This conclusion is valid

provided that a fillet with a radius of 30 μm is incorporatedat the intersection of the sidewalls with the evaporator andcondenser. Although this strategy is conceptually simple, mi-crofabrication of such fillets can pose a significant challenge[33]. Third, the deformations due to the coupled effects ofinternal pressure and temperature gradients are principallyfunctions of the CTE of the sidewall. Although these deflectionsare relatively small in comparison with the dimensions of thedevice, they exceed the tolerance of the fluid bearings sup-porting the rotor. Therefore, it is essential to explore alternatedesigns and packaging strategies to reduce deflections duringoperation.

B. Mechanical Analysis of the Rotor

The rotor in the Rankine microturbine floats on fluid bearingsand is subjected to mechanical loads from several sources. Thepressures resulting from the flows in the turbine, pump, bear-ings, and seal are distributed over the top and bottom surfacesof the rotor and can lead to bowing during operation. Also, therotor must spin at high speeds approaching 1 000 000 r/min,which results in centrifugal forces on the rotor disk and blades.The stresses and deformation due to such loads have beenanalyzed previously in the context of the Massachusetts In-stitute of Technology microengine [3], [33]. For geometriesand operating conditions similar to those experienced in theRankine microturbine, it was found that simple planar diskgeometries are adequate for the rotor but that high stresses canbe generated at the root of the blades. These blades may be


viewed as cantilevered beams subjected to bending forces dueto the centrifugal loads. Incorporating fillets at the intersectionof the blades with the rotor and ensuring a smooth surface finishafter etching are essential for ensuring reliable operation. Oneapproach for creating these fillets is to incorporate an isotropicetch after the blades have been defined by DRIE; this isotropicetch can create the desired radius of curvature at the roots of theblades [33]. In addition, the heights of the blades in the Rankinemicroturbine should be limited to 150 μm to reduce the tensilestresses at the root of these structures [34].

The rotor and blades are essentially free to expand; therefore,an increase in temperature during operation will lead to areduction of the gaps between the rotor and the surroundingstatic structure. Similar to the static structure with a temperaturedifference, the rotor exhibits a greater thermal expansion on thehot side (top), inducing a bow with upward center deflection.For typical dimensions and operating conditions, the expansionof a quartz or silica rotor is on the order of 1 μm. As discussedearlier, this value is comparable with the fluid films in the seal,pump, and bearings. Therefore, the detailed design of the deviceand its packaging must consider the deformation of both rotorand static structure to maintain functional gaps among thesecomponents over the full range of temperature. Other areas forfurther research include the reliability of the rotor in case ofaccidental impact with the sidewall during operation and wearof the rotor surfaces due to contact with the sidewall duringstartup and shutdown of the device.

VI. CONCLUSION

This paper has reported a systematic approach for the pre-liminary structural design and material selection of the secondgeneration of Rankine microturbines, which are being devel-oped for converting waste heat into electricity for portableand automotive applications. The devices may be characterizedas miniaturized pressure vessels (with a diameter of ∼1 cmand thickness of ∼2 mm) that contain high-speed rotatingcomponents (spinning at ∼1 000 000 r/min) and are subjectedto large internal pressures (∼3 MPa) and temperature gra-dients (100 ◦C/mm). This approach considers performance,reliability, and manufacturability and may be summarized asfollows.

First, the desired performance goals of the device are iden-tified within the context of the relevant thermodynamic cycleand application. Second, the primary requirements and con-straints are defined in terms of the operating conditions (max-imum pressure, temperature gradients, and rotational speeds),critical shapes and feature sizes, and microfabrication toler-ances. Third, a list of candidate materials is identified fromthe set of all engineering materials by using simple mod-els and developing material indexes [10]. This exercise canidentify qualitative tradeoffs between performance, reliabil-ity, and manufacturability. Fourth, the selection of materialsis refined by developing detailed quantitative models for theperformance of the device. These models lead to a short-ranked list of materials for different critical components. Fifth,various device configurations are analyzed to obtain a prelim-inary estimate of the reliability of the device under operating

conditions. This analysis leads to a viable set of materialsand geometries and quantifies the tradeoff between perfor-mance and reliability. Finally, the detailed design of the deviceand final material selection must account for manufacturabil-ity and the potential need for developing new processes formicrofabrication.

The models used for assessing performance and reliabilitymust ideally include the most relevant physics while mini-mizing the level of detail required since the detailed devicedesign is not yet defined. The approach used here consists ofdecomposing the system into elements that can be representedby analytical solutions, lumped models, simple numerical solu-tions, or combinations of these. Parametric studies can then helpidentify, and guide the selection of, the critical components,dimensions, and material properties before proceeding to thedetailed design.

Applying this approach and building upon the experiencegained with the first generation of the Rankine microturbine,we identified viable configurations and materials for the secondgeneration of this device for high-temperature operation. Thecylindrical sidewalls and rotor need materials with low thermalconductivity to ensure sufficient performance, and silica waschosen for these two components. The evaporator, condenser,and pumps require intricate deep etching but do not need ther-mal insulation or high mechanical strength; therefore, single-crystal silicon processed by DRIE and wafer bonding wasselected for these components. The tensile stresses due tointernal pressure and temperature gradients can be maintainedbelow critical limits if the thickness of the silica sidewall is∼100 μm, and fillets with a radius of 30 μm are incorpo-rated at the intersection of the sidewalls with the evaporatorand condenser. However, the loads applied during operationcan lead to axial and radial deflections that exceed the tol-erance of the fluid bearings that support the rotor. A com-bined analysis of the rotor and static-structure deformations,with heat transfer between the components, would thereforebe required to ensure functional operating gaps. Developingalternate packaging methods that can reduce these deflectionsis a focus of our current work. In parallel, we are also de-veloping processes for achieving the etch depths, surface fin-ish, and tolerance for microfabricating sidewalls and rotors insilica.

Based on the modeling work presented in this paper, togetherwith detailed analysis of the rotor dynamic and turbomachinerycomponents, the preliminary design of a microturbopump forexperimental demonstration at hot temperatures was completed.Fig. 12 shows a cross section of the basic structure that wasidentified as a viable configuration, and Fig. 13 shows 3-Dviews of the proposed device. Layers D and F are made usinginsulating materials (silica), while the other layers are of siliconfor ease of micromachining. The rotor and the static structurein layer D provide the axial thermal insulation required. Theinsulating layer features a honeycomb structure to maintainmechanical strength while reducing the cross-sectional areafor heat transfer through the static structure. Lateral thermalinsulation between the pump and seals/bearings is also re-quired to minimize heating of the water in the pump and isprovided by layer F. The detailed device design is beyond


Fig. 12. Cross-sectional view of the proposed hot microturbopump configuration. The insulating sidewall and rotor are formed in layer D. Layer F provideslateral insulation between the pumps and other higher temperature components. The rotor has a diameter of 4 mm. The device has lateral dimensions of 15 mmand thickness of 2.5 mm.

Fig. 13. Three-dimensional views of the proposed microturbopump configu-ration for testing at high temperatures: (a) The multiwafer device with cuts toshow the main components. (b) The rotor. (c) Detail of the rotor blades.

the scope of this paper, but this representative configurationhighlights the challenges for microfabrication, which includethe following: precision micromachining of glass rotors and theinsulating sidewall; stress relief at the junction of the sidewalland upper/lower layers; conjugate heat transfer and differentialthermal expansion in the lower layers; packaging for controlof the external thermal boundary conditions; and maintainingthe operational gaps of the fluidic components surrounding therotor.

ACKNOWLEDGMENT

The authors would like to thank Dr. C. Fuerst andDr. J. Wang for useful discussions, and P. Beauchesne-Martelfor his technical contribution.

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[34] P. Beauchesne-Martel, “Numerical analysis of subsonic laminar flowaerothermodynamics in microturbomachinery and development of a de-sign methodology,” M.S. thesis, Dept. Mech. Eng., Univ. de Sherbrooke,Sherbrooke, QC, Canada, 2009.

Mokhtar Liamini received the B.S. degree in me-chanical engineering from the National PolytechnicSchool, Algiers, Algeria, in 2002, and the M.S. de-gree in mechanical engineering with specializationin thermofluidics from the Université de Sherbrooke,Sherbrooke, QC, Canada, in 2005, where he is cur-rently working toward the Ph.D. degree and wherehe designs and fabricates Rankine microturbopumpsoperating at high temperature with a special focus onthe thermal insulation of the devices for operation athigh temperature.

Hassan Shahriar received the B.S. in mechanicalengineering degree and the M.S. degree fromMcGillUniversity, Montreal, QC, Canada, in 2007 and 2009,respectively. The focus of his Master’s thesis wason the development of a microengine for energyharvesting from waste heat.

He is currently a Sales Engineer with ENERCONCanada Inc., Montreal, QC, Canada, a companythat manufactures industrial-scale wind turbines forwind-generated power.

Srikar Vengallatore received the B.Tech. degree(with honors) in metallurgical engineering from theInstitute of Technology, Banaras Hindu University,Varanasi, India, in 1994, and the Ph.D. degree inmaterial science from the Massachusetts Institute ofTechnology (MIT), Cambridge, in 1999.

After holding postdoctoral positions at MIT, hejoined McGill University, Montreal, QC, Canada,where he is currently an Associate Professor andCanada Research Chair. His research activities focuson advanced materials and structures for microsys-

tems used in sensing, communications, and energy harvesting.Dr. Vengallatore is a member of Alpha Sigma Mu and Sigma Xi. He was

the recipient of the Class of ‘44 Award for Outstanding Teaching in 2007 andthe Early Career Research Excellence Award in 2009, both from the Faculty ofEngineering, McGill University.

Luc G. Fréchette (M’04) received the B.Ing.degree from the École Polytechnique de Montréal,Montreal, QC, Canada, in 1994, and the S.M.and Ph.D. degrees from the Massachusetts Instituteof Technology, Cambridge, in 1997 and 2000,respectively.

He is currently the Canada Research Chair inMicrofluidics and Power MEMS and a Professorof Mechanical Engineering at the Université deSherbrooke, Sherbrooke, QC. From 2000 to 2004,he was a Faculty Member with Columbia University,

New York, NY. His expertise is in microengineering of miniature systems forenergy conversion, such as heat engines (microturbines), fuel cells, coolingmicrosystems, and micro energy-harvesting devices. His activities range fromintegrated device development to more fundamental fluidic, heat, and masstransfer aspects at small scale. He also enjoys developing MEMS sensors andactuators for aerospace and other harsh environments.

Dr. Fréchette is a member of the American Society of Mechanical Engineers.

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