Design methodology for radial turbo expanders in mobile organic Rankine cycle applications q

(cid:2) We describe a detailed design methodology for ORC radial turbo expanders. (cid:2) Toluene is selected as the working ﬂuid for diesel engine waste energy recovery. (cid:2) A ﬁrst turbine of 15.5 kW is designed but yields too small inlet blade heights. (cid:2) A second turbine for minimum power generates 34.1 kW with 51.5% efﬁciency. (cid:2) A third turbine for maximum efﬁciency produces 45.6 kW at 56.1% efﬁciency. main design trade-off – efﬁciency decreases and rotational speed increases as the power requirement falls – but shows reasonable radial turbine efﬁciencies and thus practical turbo expanders for mobile organic Rankine cycle applications are realizable, even considering the compromised ﬂow geometry and high speeds imposed at such small scales. (cid:2) 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).


Introduction
The global drive towards reducing CO 2 emissions from all forms of transport will require vehicle manufacturers to develop new technology to improve powertrain system efficiency. Despite the growth of the hybrid and electric passenger vehicle segments, internal combustion (IC) engines still power the vast majority of vehicle fleets. In the case of heavy-duty on-highway trucks, and off-road machines in particular, being neither candidates for full electrification nor especially well-suited to hybridization, the ability to reduce CO 2 emissions will depend on improvements in conventional powertrains because the IC engine will continue to be the prime mover for decades to come [1].

The organic Rankine cycle for waste heat recovery
Considering that $22-35% [2] of the energy contained in the fuel is rejected to the exhaust, it is clear that waste heat recovery (WHR) technologies represent one of the best routes to achieving the required IC engine system efficiency improvements [3]. Although a significant part of the exhaust enthalpy will be extracted by turbocharging, there still exists an opportunity to recover some of the remaining lower grade heat energy. It is in this category, so-called bottoming cycles, where the organic Rankine cycle (ORC) is being investigated.
ORC has been applied to WHR in IC engines before [4][5][6][7], and even as a direct replacement for a bus engine [8], but has yet to be commercialized, with the additional cost, complexity, and packaging of a mobile ORC system so far proving prohibitive [9]. However, with the aforementioned drive towards lowering CO 2 emissions from heavy-duty vehicles, the recent US DOE-backed SuperTruck program developed a mobile ORC system for an American on-highway truck, demonstrating better than 50% brake thermal efficiency [10]. Even so, no such system is known to have been successfully applied to an heavy-duty off-road machine.

Expanders for mobile ORC systems
Selection of the appropriate expander can be made by considering the availability and temperature of the heat source, and the turbine power that can be generated. For the present application these parameters can be determined from knowledge of the range of exhaust gas mass flow rates and temperatures experienced. A comparison of radial, screw, and scroll expanders [11] suggests that for a high temperature WHR application with an expected regenerated power in the order of 15 kW, a radial machine can be considered. Other expander types have also been assessed over the years [12][13][14][15].

Working fluid selection procedure
Selection of a suitable working fluid is crucial for ORC systems [11,[16][17][18], and influences overall system performance and expander efficiency. The procedure used herein is shown in Fig. 1. Key factors in the selection process include: matching the working fluid critical temperature and that of the heat source (thereby avoiding prohibitive volume ratios across the expander [14,11]); matching the working fluid evaporating temperature and that of the heat source (to reduce irreversibilities [19]); and ensuring good chemical and thermal stability at temperatures well above operating conditions [20].
The preliminary screening step considers whether operation is at close to critical conditions. In the current work, the candidate fluids are down-selected to Toluene and Siloxanes, which have critical temperatures suitable for a $300°C heat source. Reynolds number (-) s blade span (mm) Greek letters a absolute flow angle (radians) b relative flow angle (radians) Preliminary turbine geometry calculations are performed, followed by a turbine operating point analysis that examines the effect of changing inlet conditions. The proximity of the working fluid critical conditions is considered in the final step, permitting an opportunity to adjust the operating condition with turbine performance in mind.

Working fluid requirements and selection criteria
Assumptions: Heat energy from the exhaust gases is sufficient to meet ORC operating conditions. Only pure working fluids are considered. Azeotropic and zeotropic fluids have been neglected, while acknowledging they could enable power and/or efficiency improvements [14].
No techno-economic optimization of working fluid selection is performed; the reader is referred to [21].
Fluid properties and reported advantages and disadvantages of linear Siloxanes (MM, MDM, etc.) and Toluene are presented in Table 1, and critical temperatures, pressures, and molecular weights in Table 2. For comparison, critical temperature is plotted against critical pressure in Fig. 2. The critical temperature of MM (245°C) was considered too low for the heat source temperature. Meanwhile, greater molecular weight implies a higher volumetric expansion ratio (and consequent inlet/outlet area change) across the turbine. For a small-scale, single-stage radial turbine, this should be minimized. Siloxanes with higher molecular weights (MD2M, MD3M, D4, etc.) were thus deemed unsuitable. Fig. 3 compares the evaporating and condensing temperatures of the two remaining candidates; two different pressure ratios have been plotted to examine the effect on the operating point. In general, greater pressure ratio leads to higher cycle efficiencies and lower regeneration requirements, and so it is desirable to make this as large as possible. However, a single-stage radial turbine will be limited to a pressure ratio of $25, which will limit the obtainable cycle efficiency. Fig. 3 also highlights the operating region desired for high cycle efficiency and work output, which    [14]).
ideally requires a much lower condensing temperature than the working fluids under consideration here provide. For the same pressure ratio, Siloxanes experience a much smaller enthalpy drop than Toluene, as observed for MDM in Fig. 3. This drives lower cycle efficiencies for MDM and a corresponding requirement for greater regenerator capacity to recover it [16]. Finally, considering the different working fluid attributes ( Fig. 4 and Table 3), Toluene was selected for this small-scale ORC turbine.

General considerations
Important features of the design methodology are: The working fluid is treated as a compressible, non-ideal gas, since the expansion process involves operation at close-tocritical conditions, across large expansion ratios. Flow across the expander is assumed steady and adiabatic, although the heat source will be unsteady in a mobile application, and there will inevitably be some degree of heat loss.
The number of stages is limited to one to minimize complexity and cost. Radial-fibred blades are not required since material strength is not considered a limiting factor, due to the relatively low enthalpy changes and peripheral speeds. Full admission is initially assumed. If blade heights are unsatisfactory under full admission, partial admission will be considered.

Performance parameters
Total-to-static isentropic efficiency is used since it is assumed that rotor outlet kinetic energy will not be recovered. In Eq. (1), h 01 denotes the stage inlet stagnation enthalpy, and h 3act and h 3is the actual and isentropic outlet static enthalpies, respectively.
The volume flow rate ratio V R (Eq. (2)) has a major impact on turbine efficiency and geometry; the high values experienced in the expansion process of organic fluids necessitate a large change in rotor blade height between the inlet and outlet stations.
The specific speed N s (Eq. (3)) is often employed as a standard index to correlate the flow capacity to the work output of any particular turbomachine [25], and can be used to provide an expectation of attainable efficiency.
The size parameter SP (Eq. (4)) was introduced [17] to indicate the relative size of competing designs, and can be used in a similar fashion to the specific diameter [25,26].

Design parameters
As the inlet blade speed U 2 is limited by mechanical stress considerations (independent of turbine size), high rotational speeds are to be expected in turbines with diameters in the order of a few centimeters. It is used here as a main design variable -changing U 2 essentially increases or decreases the inlet relative flow angle b 2 -and a wide range is usually considered in order to explore the effect on rotor performance.
The degree of reaction K (Eq. (5)) is the ratio of static enthalpy change occurring across the rotor to the total enthalpy change across the stage as a whole. The lower the reaction, the larger the acceleration across the stator.
The blade loading coefficient W (Eq. (7)) represents the work capacity of a turbine stage, defined as the ratio of the total specific enthalpy change to the square of the blade speed [25,26].

Targets, assumptions, and constraints
Various targets, assumptions, and constraints on the rotor design are collated in Table 4. Allowing for the energy extracted by the turbocharger, the temperature of the exhaust gas at the heat exchanger inlet will be $300°C giving an energy transfer rate to the ORC system in the range 125-145 kW, based on example engine data [2]. Applying typical cycle efficiencies of 12-18% (as reported by [13,16]) suggests a turbo expander power requirement of 15-26 kW, an approximation that suffices for the purpose of this study. The assumptions and constraints applied to rotor geometry (including the velocity triangles) and operation are given in Table 5.

Velocity triangle design
Fig . 5 shows the standard rotor meanline cross-section of a 90 radial inflow turbine. The stage numbering specified here is used throughout this article.

Rotor inlet conditions
The rotor inlet velocity triangles are constrained by the limit imposed on the inlet relative Mach number M w2 , which in turn constrains the inlet relative velocity W 2 . Applying the minimum blade speed U 2 min , calculated using Eq. (10), as an initial condition, the inlet velocity triangle is fully defined (Fig. 6).
As the inlet blade speed is increased from U 2 min , the degree of reaction increases (for fixed U) as a result of decreasing absolute inlet velocity C 2is and thus increasing rotor inlet static enthalpy h 2 . The absolute inlet velocity considered in this calculation is the isentropic velocity C 2is , which is related to the actual velocity  Table 5 Rotor design constraints (Toluene as working fluid).
To analyze the effect of K on the inlet velocity triangle and blade geometry, a range of blade speeds (see Table 5) were considered. Eq. (5) shows K is dependent on the outlet static enthalpy h 3act , i.e., the outlet conditions will have an impact, and will need to be determined to fully assess the effect of design parameters on the rotor geometry.

Rotor outlet conditions
The flow coefficient U and the ratio of blade speed to spouting speed U 2 =C 0 (the ''velocity ratio'') need to be determined. These parameters are correlated in Fig. 7 to provide an estimate of the efficiency, at least for conventional radial turbines [30]. The figure indicates a velocity ratio range of 0:6 < U 2 =C 0 < 0:75, and a flow coefficient range of 0:2 < U < 0:4 should generate the highest efficiencies. Although this will not be valid for ORC turbines, a similar trend is assumed to establish a starting point in the present work.
In contrast to the inlet rotor conditions, for which velocity triangles have yet to be fixed, it is assumed that the rotor outlet will contain zero swirl. This imposes the velocity relationship shown in Fig. 8; after selecting a flow coefficient U, and having knowledge of the outlet stagnation enthalpy, the static enthalpy (for each flow coefficient) can be determined from Eq. (12).
From the outlet velocity triangle, Eq. (14) can be derived [25]. This expression is used to obtain the outlet flow angle b 3av at the mean radius. As previously mentioned, the ratio r 3av =r 2 is used as an input variable, so by considering a range of flow coefficients, different outlet velocity triangles may be obtained. Fig. 9 shows a flow chart of the velocity triangle design procedure, including the method to determine the outlet velocity triangle.

Determining the density at stator outlet
The calculated degree of reaction is then used as an input in an Excel program, which imports relevant fluid properties from REFPROP [24] to calculate the stator outlet enthalpy (i.e., rotor inlet h 2 ) and density. The outlet meridional velocity C m3 , together with the inlet and outlet total enthalpies h 01 and h 03 are required as inputs in order to perform calculations using the definition of reaction in Eq. (5).
3.6. Geometry design 3.6.1. Geometrical and effective area Employing mass conservation, the annular inlet area A geom 2 can be obtained from Eq. (15) by assuming a mass flow rate _ m, knowing the inlet density q 2 and the inlet meridional velocity C m2 .    7. Attainable efficiency levels of radial inflow turbines [30]. Reprinted with permission of ASME. Since the full peripheral (at the inlet) or annular (at the outlet) areas are not available due to the presence of the blades, a blockage coefficient B is introduced, e.g., at the rotor inlet the geometrical area A geom2 and the effective area A f2 are related by Eq. (16).
The blockage coefficient accounts for the area due to the blade thickness t, computed using Eq. (17), where Z b is the blade number and s is their span. Fig. 10 illustrates the blockage effect at the rotor exit.
Even though B 2 will change between individual designs, a single value (refer to Table 9) has been assumed for the geometries calculated here. Knowing the inlet effective area A f2 , the inlet radius r 2 can be determined by assuming a value for the inlet span s in Eq. (18).
This defines the inlet geometry. The outlet geometry is then calculated using Eq. (19) and knowledge of the outlet density q 3 and an assumed value of C m3 (which depends on the selected values of A larger value for the outlet blockage coefficient B 3 was chosen (see Table 9) to calculate the effective outlet area A f3 , since the blades occupy a larger portion of the outlet flow area, compared to the inlet. The calculation of B 3 is not as straightforward, since a streamwise analysis would need to be performed before the actual outlet geometry is completely defined. The outlet shroud and hub radii are calculated by assuming a value for the hub to shroud radius ratio, r 3h =r 3s , as per Eq. (20).

Blade number
In order to calculate the blade number, the empirical relationship of Glassman (Eq. (21)) is employed [25].
The full procedure used to establish the rotor geometry is given in Fig. 11.

Performance prediction by loss coefficient evaluation
A prediction of turbine performance based on geometrical parameters is required to evaluate competing designs. For conventional radial turbines, a loss analysis can be employed based on the calculation of a number of loss coefficients [31]. Their application to organic fluids is discussed below.

Incidence loss
Incidence loss will be based on the change in the tangential component of kinetic energy [as per 26,31]. The optimum relative flow angle b 2;opt is defined as that at which there is no change in the tangential velocity component [31], computed using Eq. (22).
The incidence loss is then expressed as an enthalpy change (later represented as an efficiency deficit), in Eq. (23) [as per 25], where the exponent n depends on whether the incidence is positive or negative (n ¼ 2:5 for i > 0; n ¼ 1:75 for i < 0).

Nozzle loss coefficient
The nozzle loss coefficient is defined in [25] as: The velocity coefficient (Eq. (11)) is related to the enthalpy loss coefficient through: For well-designed stators in conventional turbines, / N ranges between 0.90 and 0.97 [25]. An intermediate value of 0.95 is selected as an initial guess in the design procedure. The selection of a nozzle loss coefficient establishes the nozzle efficiency as: The effect of f N is to reduce the absolute rotor inlet velocity and therefore the meridional inlet velocity, consequently increasing the ratio C m3 =C m2 across the rotor.

Rotor loss coefficient
In the case of ORC turbine design, the rotor loss coefficient will be defined in such a way to absorb other losses and is expressed in [25] as: The velocity coefficient is given as: This is related to the enthalpy loss coefficient through: For well-designed rotors in conventional turbines, / R ranges between 0.70 and 0.85 [25]. In contrast to the treatment of the stator velocity coefficient, there is no need to assume a value for the rotor loss coefficient f R , since a value for the initial isentropic efficiency has already been defined.

Tip clearance loss
For the cases considered here, involving extremely small spans, the radial clearance must be reduced to 0.25 mm to maintain the tip leakage within acceptable levels. Several empirical models for clearance loss have been proposed. An expression in terms of inlet blade height and the ratio of outlet to inlet mean radii, and the radial clearance r , is given in [32] as:

Windage loss
The loss of specific work due to the windage can be expressed [26] as: 3.7.6. Shock loss The rotor inlet relative Mach number M w2 has been limited to 0.96, and thus transonic flow will occur across the rotor stage. As sonic conditions are reached at the stator outlet, shock losses will take place at the rotor entry and through the passage, and are also likely to be present at rotor outlet. The expressions found in the literature [26, e.g.] rely on ideal gas laws and cannot be applied here. Additionally, the conventional method for accounting for shock losses may not be applicable to organic fluids operating near critical conditions. Hence it is worth considering that additional losses will be present and that the true isentropic efficiency is expected to be lower than that predicted in this study.

Design results
Three different radial turbine designs are now presented: (i) a small turbine designed to meet the low power requirement, (ii) a medium turbine, also designed for minimum power but which meets an additional geometry constraint on inlet blade height, and (iii) a large turbine meeting the same constraints as (ii) but designed for maximum isentropic efficiency. Note that the labels small, medium, and large are only used here to clearly distinguish the three designs, rather than as an indication of size.

Small turbine
This option was designed for the low end of the expected turbine power requirement (15-26 kW). In Fig. 12 both the span and rotational speed increase with the flow coefficient U. The higher the inlet blade speed, the smaller the span for the same flow coefficient (and the higher the rotational speed). So a high U and a small U 2 are beneficial to promote larger inlet blade heights, especially important at this small scale, but at the cost of higher rotational speed and smaller inlet and outlet radii. Nevertheless, by selecting the minimum possible blade speed of 301.9 m s À1 (which corresponds to an axial inlet to the stage, i.e., the minimum blade speed without pre-swirl), the rotational speed can be reduced somewhat, while the span can be increased.
Operating point and geometrical data for the resulting 15.5 kW turbine are listed in the first data column in Table 9. In this case, the design is specified such that the largest possible inlet blade height is generated whilst complying with all other design constraints. Despite this, the resulting inlet blade height of 1.6 mm is still too small to be practical, and so the estimation of isentropic efficiency was not carried out and hence is not included. The inlet and outlet velocity triangles at mean radius for this turbine are shown in Fig. 13, together with an illustration of the rotor geometry in the meridional plane. The resulting shape is mainly due to the imposed design constraints, which limit the outlet-to-inlet tip radius ratio to a maximum of 0.95, giving rise to a blade profile that has significant sections of constant shroud radius. The significant change in density across the passage is the reason for the large variation in blade height.
The hub and shroud outlet velocity triangles shown in Fig. 14 were calculated using the assumptions of constant axial velocity (C m3 ) and constant rotational speed along the radius. All velocity triangle parameters for this turbine can be found in Table 6, where it can be seen that a higher relative velocity (and Mach number) is reached at the shroud. Increasing the flow coefficient U raises the outlet meridional velocity C m3 and thus reduces the outlet relative flow angle b 3 . Since the outlet blade speed U 3 remains close to constant, the outlet relative velocity W 3 will also increase.
Increasing the blade loading coefficient W leads to a decrease in inlet meridional velocity C m2 , an increase in the inlet relative flow angle b 2 , and a decrease in the inlet tangential velocity C h2 and absolute flow angle a 2 . This also leads to an increase in reaction, which increases the density ratio across the rotor passage. The same effects apply for both this small turbine, and the medium and large turbine designs that follow. ig. 13. Rotor geometry, inlet and outlet velocity triangles at mean radius -small turbine.

Medium turbine
This turbine has been designed with the objective of minimizing power output, while requiring a reasonable rotor geometry. Fig. 15(a) shows that the rotational speed of the turbine is strongly affected by the choice of flow coefficient (U), yet is quite insensitive to the blade speed (U 2 ), within the range shown. This is because a higher U will generate greater outlet static enthalpy and higher reaction. This in turn leads to higher inlet density and thus a smaller inlet radius, as indicated by Fig. 15(b). So, the higher the U, the smaller the mass flow rate required to comply with the design constraints, and thus to target minimum power output, a higher U is beneficial for generating reasonable rotor geometries.
To recap, the inlet blade height of the small turbine was too small. Hence the medium turbine has been designed to generate   the lowest power output while maintaining a minimum inlet blade height of 2 mm, representing the minimum feasible value for wheel manufacture. The rest of the specification has been carried forward, i.e., the inlet and outlet velocity triangles are identical to those for the small turbine (refer to Fig. 13). Even though the small and medium turbines have the same inlet and outlet velocity triangles at mean radius, those at the outlet of the hub and shroud will differ due to the change in rotor geometry, as listed in Table 7.
The resulting performance and geometrical data for this 34.1 kW turbine are shown in the second data column in Table 9. This design has a lower rotational speed but the density ratio is much higher compared to the small turbine, but there is only a slight change in tip radius between inlet and outlet of the rotor passage. This is due to the outlet to inlet tip radius ratio constraint, stated in Table 9, which is intended to reduce blade curvature. Although this generates small blade heights, not constraining this ratio will lead to unreasonable geometries. Fig. 16 shows the rotor blade profile for the medium turbine is not too dissimilar from that for the small turbine. While the radii and axial length of the medium turbine have grown to accommodate the increase in power output, the geometrical constraints are the same as before, except for the imposed 2 mm minimum inlet blade height. Fig. 17(a) shows that the higher the flow coefficient U, the lower the isentropic efficiency (for a given blade speed). This is primarily due to rising rotor (and nozzle) losses with increasing outlet velocities (and thus with increasing U). If the blade speed is increased, there will be a detrimental effect on the flow coefficient and, to a much lesser extent, the passage loss coefficient.

Large turbine
Increasing the blade speed for a given U leads to higher isentropic efficiencies however, due to the lower level of incidence loss, as illustrated in Fig. 17(b).
Hence to generate a high efficiency design, a lower flow coefficient was selected, and the blade speed (U 2 ) was permitted to increase since less incidence loss will be experienced at higher speeds, again giving rise to higher isentropic efficiency (which can be considered insensitive to U). The final constraint applied to this design was an upper power limit of $45 kW. The resulting design and operating performance parameters for a turbine designed for maximum efficiency while meeting the stated constraints are given in the third data column in Table 9. The rotational speed has now dropped to $71.5 k min À1 , and the predicted isentropic efficiency has increased by almost five points, to 56%. The inlet and outlet velocity triangles at mean radius for   this design are illustrated alongside the blade geometry in Fig. 18. Outlet velocity triangles for the hub and shroud are shown in Fig. 19. All velocity triangle parameters for this design are listed in Table 8.

Large turbine performance analysis
The optimum incidence angle, b 2;opt , can be calculated using Eq. (22). The relationship between the optimum incidence angle and the inlet absolute flow angle is plotted in Fig. 20. The values obtained for both a 2 and b 2;opt are within the same range as those seen in conventional radial inflow turbines [31]. The trend followed is also similar, although a smaller variation in b 2;opt is observed. Fig. 21 shows the decrease in g t-s caused by the combination of the different loss contributions. It can be observed that the incidence loss decreases with increasing U 2 , whilst the windage loss remains relatively constant throughout, and the passage losses increase with increasing U 2 , the largest contribution coming from the latter. Note that Fig. 21 is most representative of the medium turbine since the loss data is plotted for a flow coefficient of 0.4. Indeed, Fig. 21 shows that the isentropic efficiency at a inlet blade speed of 302 m s À1 (that of the medium turbine, Table 6) is $52%, which agrees with the value calculated for the medium turbine (51.5% in Table 9). Table 10 compares the large turbine against similar designs from the literature. Despite similar power outputs, the comparison designs are geometrically quite different, likely due to different working fluids and design constraints. However a large change in blade height from inlet to outlet, and a correspondingly small change in tip radius, is characteristic of all designs.

Comparison with ORC radial turbo expanders in the literature
Comparison Turbine 1 [27] accommodates inlet pre-swirl (b 2 is positive). Pre-swirl has not been considered here to avoid the significant impact on incidence loss, but it does permit smaller values of U 2 . Although Comparison Turbine 2 [15] has an efficiency of 79%, the blade inlet height is only 1.6 mm. In a further example, the 0.7-0.8 mm blade heights specified for a mini-ORC system using     Toluene as the working fluid [16] are also not considered practical, nor is the rotational speed of 182.3 k min À1 . Fig. 22 shows the values of g t-s predicted for the ORC turbines as a function of the flow coefficient U, which are much lower than can be achieved by conventional turbines [30]. One of the main differences between the radial inflow turbines in this study and that presented in Table 11 is the much lower pressure ratio experienced across the conventional radial turbine. The maximum specific work done across a single stage would limit the pressure ratio across a conventional turbine expanding air or exhaust gas. The change in inlet to outlet tip radius in ORC turbine designs is much smaller than for the conventional turbine, leading to different rotor geometries.

Conclusions
This work developed a procedure for the design of practical radial turbo expanders for mobile ORC applications, recognizing the interdependence between expander design and working fluid selection, using the REFPROP database [24] to account for real gas effects. Siloxanes and Toluene were down-selected due to their high critical temperatures, which align with the $300°C heat source; Toluene was identified as the more suitable overall.
Three different turbine designs were presented: a small turbine ($20 mm dia.) generating 15.5 kW at $136 k min À1 that meets the low power requirement but requires a $1.6 mm inlet blade height; a more practical medium turbine (62.9 mm) producing 34.1 kW with 51.5% efficiency at $91.7 k min À1 ; and a large turbine (83.0 mm) making 45.6 kW at $71.5 k min À1 , designed for maximum isentropic efficiency (56.1%). These show that reducing the power level compromises isentropic efficiency, with the largest loss contributions originating in the rotor and nozzle passages. A major issue for small-scale ORC radial turbines is the high inlet density and density ratio, leading to extremely small inlet blade heights of a few millimeters, and a large variation between inlet and outlet blade heights.
The novelty of the current work lies in the combination of: (i) the down-selection of Toluene as the working fluid, (ii) the design of radial turbo expanders with explicit provision of the loss equations and procedure employed, and (iii) its application to WHR in a mobile, heavy-duty off-road diesel engine. Future work will integrate the turbine design methodology within a larger ORC design process, comprising a 1D engine model (simulating the transient heat source) and a thermodynamic system model, and will refine the turbine design in 3D CFD. Once these components are in place, it should be feasible to optimize ORC turbo expander design and overall cycle efficiency over a real-life machine duty cycle. Fig. 22. Predicted large ORC turbine performance (red circles) plotted against conventional radial turbine performance (contours) [30]. Reprinted with permission from ASME. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 11
Comparison of the large ORC and conventional (air) radial turbine designs in the range 40-50 kW.