**1.1 State of art**

4 Efficiency, Performance and Robustness of Gas Turbines

conditions, and system identification techniques are presented. Practical recommendations

In this chapter a summary of the gas turbine simulator development and its model characteristics are described. Stochastic and discrete events models are not considered, but deterministic models of industrial processes are contemplated. The simulator was tested in all the operation range from cold start to 100% of load and fulfils the performance specified

Many different methods exist to integrate various design elements into an overall process. Ideally, designers like to perform all design steps concurrently in order to minimize the overall time required to conduct a study. Whole books have been written to address each of steps involved in design of gas turbines, so this book cannot possible cover all issues.

The book covers many aspects of gas turbine design and operation. The book represents the latest research of various groups of internationally recognized experts in gas turbine studies. This book is intended for engineers and technical workers in design, optimisation and maintenance of gas turbines, and specialists is thermodynamics and heat transfer, particularly those involved with energy systems and transportation systems that make use of gas turbines. It will be of interest to academics working in aeroengine control and to industrial practitioners in companies concerned with design of gas turbines. The works presented in the book are easily extendible to be relevant in other area in which gas turbines

The open exchange of scientific results and ideas will hopefully lead to improved reliability of gas turbines and aeroengines. The book presents necessary data and helpful suggestions to assist scientists and engineers involved in the design, selection and operation of gas

Hopefully, it has at least introduced the reader to tools that are currently available.

are given to develop an effective condition monitoring system.

**9. Models for training on a gas turbine power plant** 

by the client, including a comparison of its results with plant data.

play a role such as power engineering and marine engineering.

**10. Summary** 

turbines.

Object of the present work is the detailed study, in every its aspect, of Ultra-Micro-Gas-Turbine Generator, that is a power device with high power density. These generators, although the covered power range oscillates between 100 and 500W, is characterized by very reduced overall dimensions: this introduces complications in the design and, above all, the realization of the mechanical components who represents the greater difficulty to exceed. The advanced searches in this field preview the realization of the characteristic structures of the machine with high tech systems:


Fig. 1. Typical compressor a) and b) turbine D geometry [Epstein 2003]

Ultra Micro Gas Turbines 7

Since 90's, the academic world started to study the possibility to realize a "micro" gas turbine (GT) set, with an overall dimensions of the order of the centimetres, able to developing a nominal power within 0.10 to 100 kW. Such a type of apparatus are defined today "micro gas turbine". At the moment, the larger GT sets in service are characterized by a radial dimensions of the order of the meter and develop hundred of MW of nominal power, while the generator of a UMGT is large few millimetres, for which the elaborated mass flow rate by the micro device will be 10-6 times lower than a conventional machine, if the same tip speed is maintained. Moreover, the generated power will be 10-6 lower, consequently a micro GT device would be able, in first analysis, to producing about hundred of Watts. This value re-enters in the extremely extended field of the portable equipment applications in which the battery packages represent the main solution to the problem. The obtainable power density is greater than a conventional battery package, thanks to the fact that the power scales with the flow rate and ,therefore, with the square of

Conceptually it is possible to realize any thermodynamic cycle to these scales, but it is necessary to remind that the reduced dimensions do not allow the possibility to insert any components characterized by particularly complex geometries. This consideration forces the research to adopt a simple Brayton cycle. Other considerations concern the fluid dynamical behaviour of the device and the mechanics of the machine, which will modify the relative choices to the thermodynamic cycle, moving the optimal design parameters in different zones from those developed for a classic large scale machine. In fact, while the speed and the temperatures are almost unchanged regarding the macro turbines, the chord blade is of the order of millimetre. The consequence is that the value of Re number is lower than the actual conventional large scale turbo machines (usually between 105 - 106). Viscous forces will have greater influence and the relative losses will be more evident. The losses linked to the three-dimensional aspect of the device, to the clearance between case and disc or to shock waves will be more significant and higher than the common ones. It is reasonable to think that the increase of the viscous forces produces higher losses for aerodynamic resistance in the piping and/or manifolds. One of the problems that the research/designer must be faced in the study of the micro fluid dynamic phenomena is the adequacy of the continuous fluid model. To evaluate the possibility of adopting the Navier-Stokes equations, the Knudsen number Kn, equal to the ratio between the free medium path of particles and

<sup>2</sup> P L ∝ (1)

<sup>3</sup> V L ∝ (2)

P/V 1/L ∝ (3)

• Air mass flow rate: ≈ 2 g/s • Rotational speed: ≤ 300 000 rpm

the length, while the volume with the cube:

• Net power: 4 ÷ 100 W

• TIT: ≈ 1300K

**2. Scaling factor** 

so:

Fig. 2. Typical 2D combustor

Fig. 3. MIT prototype [Epstein 1999 & 2003]

In figure 3 it shown a prototype realized from the M.I.T., that can be consider as the "symbol/emblem" of these researches carried out during the last few years in microturbines. It is constituted by a overlapping layers in sequence, starting from the compressor, the toroidal combustion chambers and the turbine. The characteristic data of this prototype can be reassumed in:


We can notice the temperatures reached in these systems are higher than those characteristics of the actual large scale systems. Therefore, in the zones affected by the highest thermal stresses, the Silicon Si has been replaced with the most resistant SiC material. This prototype represents the highest state of the technique and the more advanced research that can be reached in this moment. Other examples of UMGT exist, however, thus do not characterized by exasperated technological levels and with a similar structure to the conventional systems. Also regarding the used materials, these device use typical steels of the commercial impellers. The thermodynamic parameters are similar to large scale sets:

• Compression ratio: ≤ 3


In figure 3 it shown a prototype realized from the M.I.T., that can be consider as the "symbol/emblem" of these researches carried out during the last few years in microturbines. It is constituted by a overlapping layers in sequence, starting from the compressor, the toroidal combustion chambers and the turbine. The characteristic data of this prototype

**TURBINE** 

**COMPRESSOR** 

**Air path** 

**outlet** 

**20 mm**

**inlet** 

We can notice the temperatures reached in these systems are higher than those characteristics of the actual large scale systems. Therefore, in the zones affected by the highest thermal stresses, the Silicon Si has been replaced with the most resistant SiC material. This prototype represents the highest state of the technique and the more advanced research that can be reached in this moment. Other examples of UMGT exist, however, thus do not characterized by exasperated technological levels and with a similar structure to the conventional systems. Also regarding the used materials, these device use typical steels of the commercial impellers.

Fig. 2. Typical 2D combustor

**Fuel injec�on** 

Fig. 3. MIT prototype [Epstein 1999 & 2003]

**Combus�on chamber** 

can be reassumed in: • Fuel: Hydrogen

• Power: 4 ÷ 10W

• TIT: 1600 K

• Fuel consumption: 16 g/h

• Rotational speed: ≈106 rpm

• Used materials: Si And SiC

• Compression ratio: ≤ 3

The thermodynamic parameters are similar to large scale sets:

• Net power: 4 ÷ 100 W

### **2. Scaling factor**

Since 90's, the academic world started to study the possibility to realize a "micro" gas turbine (GT) set, with an overall dimensions of the order of the centimetres, able to developing a nominal power within 0.10 to 100 kW. Such a type of apparatus are defined today "micro gas turbine". At the moment, the larger GT sets in service are characterized by a radial dimensions of the order of the meter and develop hundred of MW of nominal power, while the generator of a UMGT is large few millimetres, for which the elaborated mass flow rate by the micro device will be 10-6 times lower than a conventional machine, if the same tip speed is maintained. Moreover, the generated power will be 10-6 lower, consequently a micro GT device would be able, in first analysis, to producing about hundred of Watts. This value re-enters in the extremely extended field of the portable equipment applications in which the battery packages represent the main solution to the problem. The obtainable power density is greater than a conventional battery package, thanks to the fact that the power scales with the flow rate and ,therefore, with the square of the length, while the volume with the cube:

$$\mathbf{P} \approx \mathbf{L}^2 \tag{1}$$

$$\mathbf{V} \approx \mathbf{L}^3 \tag{2}$$

so:

$$\mathbf{P} \;/\; \mathbf{V} \approx \mathbf{1} \;/\; \mathbf{L} \tag{3}$$

Conceptually it is possible to realize any thermodynamic cycle to these scales, but it is necessary to remind that the reduced dimensions do not allow the possibility to insert any components characterized by particularly complex geometries. This consideration forces the research to adopt a simple Brayton cycle. Other considerations concern the fluid dynamical behaviour of the device and the mechanics of the machine, which will modify the relative choices to the thermodynamic cycle, moving the optimal design parameters in different zones from those developed for a classic large scale machine. In fact, while the speed and the temperatures are almost unchanged regarding the macro turbines, the chord blade is of the order of millimetre. The consequence is that the value of Re number is lower than the actual conventional large scale turbo machines (usually between 105 - 106). Viscous forces will have greater influence and the relative losses will be more evident. The losses linked to the three-dimensional aspect of the device, to the clearance between case and disc or to shock waves will be more significant and higher than the common ones. It is reasonable to think that the increase of the viscous forces produces higher losses for aerodynamic resistance in the piping and/or manifolds. One of the problems that the research/designer must be faced in the study of the micro fluid dynamic phenomena is the adequacy of the continuous fluid model. To evaluate the possibility of adopting the Navier-Stokes equations, the Knudsen number Kn, equal to the ratio between the free medium path of particles and

Ultra Micro Gas Turbines 9

for radial pumps and compressors- was much more sensitive to additional factors, e.g. the different relative roughness of the full-scale machine with respect to the model, leakage effects due to the geometric non-similarity of machining tolerances and clearances, and both the lack of data and the excessive measurements uncertainty in the smallest models. There have been numerous attempts to formulate a general model of η = f (Re) scaling, but all the proposed models agree with the experimental data only within a limited range of configurations and fall therefore short of representing general design correlations. The main problem of the available formulations seems to be on the one side their complexity and on the other side the non-crisp phenomenological model they subsume, but the common point in all approaches is the distinction in Reynolds dependent and independent efficiency losses. This assumption leads to unavoidable difficulties in the determination of the Reindependent loss fraction, mostly originated by non-homogeneous factors like manufacturing methods, tolerances and clearances. An interesting series of experimentally validated studies were conducted in the 80's for single and multistage centrifugal compressors by Wiesner [Wiesner 1979], Casey and Strub: the results of these investigations differ from Author to Author, as do their respective conclusions, but one common point all agreed upon is the definition of a reference Reynolds number based on the width of the exit

> U b2 2 Re ν

By contrast, since we are interested here in introducing correction factors to the Balje charts, it was necessary to adopt the same choice of parameters: therefore, in this work the *Re*

> U D2 2 Re ν

Some scaling formulations include the influence of Reynolds number and surface roughness, but in this work we consider only hydraulically smooth surfaces, eliminating thus the roughness variable from the picture, also in consideration of the rather scant data available on the few prototypal rotors in the ultra-micro scale range. The derivation of a "universal" formula is intrinsically difficult, due to the substantial difference in the flow phenomenology, so that each class of machines requires a specific analysis. The objective of this work is to propose a preliminary method to scale the efficiency of ultra-microcompressors and turbines, investigating the possibility to extend the applicability of Balje

charts for miniaturized machines, to reduce design time- and resources investment.

**3.1 Reynolds number effects – Problem formulation and coefficient definition** 

ref

η

η

The general functional relationship proposed in the available references is of the so-called

<sup>1</sup> Re a 1a 1 Re

Whereas the coefficients *a* and *n* differ from Author to Author, as represented in Table 1.

( )

n ref

<sup>−</sup> =+ − <sup>−</sup> (6)

definition as reported in [Balje 1981] has been used throughout:

<sup>=</sup> (4)

<sup>=</sup> (5)

section:

Stodola form:

characteristic length, can be used. Several tests have evidence that the first effects of the non-continuity appear for values of Kn = 0,1, while the continuous model loses its validity to Kn = 0.3. Considering that the free medium path of the air, at atmospheric conditions, is 70 nm (nanometres), the flow will have to be considered discontinuous for lengths of 0.2 µm. The considered micro devices dimensions (the gap will be of the order of some µm) the flow can be still studied as continuous, therefore it is not necessary to consider the molecular kinetic. The heat exchange between the device components and with the fluid is higher, due to the small scales of length, for which the thermal gradient will be lower and consequently thermo-mechanical stress will be lower. On the other hand, the parts isolation will be more complex and the heat losses towards the outside will be higher. The materials deserve a detail attention since the reduced scales allow the introduction of light ceramic material, with very attractive mechanical properties, but - to large-scale -unusable for the GT construction. With these dimensions, in fact, the material can be still considered as a continuous one, for which the plastic, the elastic, the creep and the oxidation behaviour, and finally the coefficient of thermal conduction, do not change, while the mechanical resistance is greater, strongly dependent on the manufacturing defects that are "naturally" limited by the micro-dimensions.

### **3. Thermodynamic cycle**

Generally, the thermodynamic analysis of a system is independent by the scaling factors; theoretically it is possible to adopt any type of cycle to the micro-scales without particular attention. The technological limits, the inherent mechanical and fluid dynamical considerations and the necessity of device compactness, impose limited and important choices. In the case of the UMGT, it has been decided to privilege, fundamentally, the compactness and simple manufacturing, to contain the costs, admitting not optimal machine efficiency. This choice does not involve any particular disadvantages, since from theoretical extrapolations show sufficient efficiencies, to obtain higher energy density than to the best actual battery packages. The thermodynamic cycle adopted, in terms of simplicity, is the Brayton cycle, that has moreover the advantage to supply increasing energy density with the increase of the operational speed. The main disadvantage is the necessity in such case to have a component efficiency at least to the 40-50% for being self-sustainable: it must, therefore, be headed at most efficient and possible productive technologies. The state of the art for thus small structures renders the integration of conventional cooled or regenerated cycles improbable, but remains the possibility to use the outlet fluid of the compressor to cool the walls of the combustion chamber, or to obtain a sort of pre-heating, without to complicate geometry. To obtain a thermodynamic cycle adapt to the prefixed scope, the outlet temperatures of the combustion chamber must be comprised between 1200-1600 K and the tip speed between 300-600 m/s, consequently stresses will be of the 102 order of MPa for compression ratios between 2:1 and 4:1. Wanting, at least, to privilege compactness and lightness the choice of radial machine is most suitable, thanks the possibility to use a single stage for compressor and turbine. The influence of the Reynolds number on the performance of turbo machines has received considerable attention in literature, and several more or less general and sufficiently reliable models have been demonstrated, both for incompressible and compressible flows. Historically, the first formulations originated from empirical data collected on hydraulic turbine models and yielded acceptable results for fullscale applications. It is clear that the scaling for other types of machinery -and specifically

characteristic length, can be used. Several tests have evidence that the first effects of the non-continuity appear for values of Kn = 0,1, while the continuous model loses its validity to Kn = 0.3. Considering that the free medium path of the air, at atmospheric conditions, is 70 nm (nanometres), the flow will have to be considered discontinuous for lengths of 0.2 µm. The considered micro devices dimensions (the gap will be of the order of some µm) the flow can be still studied as continuous, therefore it is not necessary to consider the molecular kinetic. The heat exchange between the device components and with the fluid is higher, due to the small scales of length, for which the thermal gradient will be lower and consequently thermo-mechanical stress will be lower. On the other hand, the parts isolation will be more complex and the heat losses towards the outside will be higher. The materials deserve a detail attention since the reduced scales allow the introduction of light ceramic material, with very attractive mechanical properties, but - to large-scale -unusable for the GT construction. With these dimensions, in fact, the material can be still considered as a continuous one, for which the plastic, the elastic, the creep and the oxidation behaviour, and finally the coefficient of thermal conduction, do not change, while the mechanical resistance is greater, strongly dependent on the manufacturing defects that are "naturally" limited by the

Generally, the thermodynamic analysis of a system is independent by the scaling factors; theoretically it is possible to adopt any type of cycle to the micro-scales without particular attention. The technological limits, the inherent mechanical and fluid dynamical considerations and the necessity of device compactness, impose limited and important choices. In the case of the UMGT, it has been decided to privilege, fundamentally, the compactness and simple manufacturing, to contain the costs, admitting not optimal machine efficiency. This choice does not involve any particular disadvantages, since from theoretical extrapolations show sufficient efficiencies, to obtain higher energy density than to the best actual battery packages. The thermodynamic cycle adopted, in terms of simplicity, is the Brayton cycle, that has moreover the advantage to supply increasing energy density with the increase of the operational speed. The main disadvantage is the necessity in such case to have a component efficiency at least to the 40-50% for being self-sustainable: it must, therefore, be headed at most efficient and possible productive technologies. The state of the art for thus small structures renders the integration of conventional cooled or regenerated cycles improbable, but remains the possibility to use the outlet fluid of the compressor to cool the walls of the combustion chamber, or to obtain a sort of pre-heating, without to complicate geometry. To obtain a thermodynamic cycle adapt to the prefixed scope, the outlet temperatures of the combustion chamber must be comprised between 1200-1600 K and the tip speed between 300-600 m/s, consequently stresses will be of the 102 order of MPa for compression ratios between 2:1 and 4:1. Wanting, at least, to privilege compactness and lightness the choice of radial machine is most suitable, thanks the possibility to use a single stage for compressor and turbine. The influence of the Reynolds number on the performance of turbo machines has received considerable attention in literature, and several more or less general and sufficiently reliable models have been demonstrated, both for incompressible and compressible flows. Historically, the first formulations originated from empirical data collected on hydraulic turbine models and yielded acceptable results for fullscale applications. It is clear that the scaling for other types of machinery -and specifically

micro-dimensions.

**3. Thermodynamic cycle** 

for radial pumps and compressors- was much more sensitive to additional factors, e.g. the different relative roughness of the full-scale machine with respect to the model, leakage effects due to the geometric non-similarity of machining tolerances and clearances, and both the lack of data and the excessive measurements uncertainty in the smallest models. There have been numerous attempts to formulate a general model of η = f (Re) scaling, but all the proposed models agree with the experimental data only within a limited range of configurations and fall therefore short of representing general design correlations. The main problem of the available formulations seems to be on the one side their complexity and on the other side the non-crisp phenomenological model they subsume, but the common point in all approaches is the distinction in Reynolds dependent and independent efficiency losses. This assumption leads to unavoidable difficulties in the determination of the Reindependent loss fraction, mostly originated by non-homogeneous factors like manufacturing methods, tolerances and clearances. An interesting series of experimentally validated studies were conducted in the 80's for single and multistage centrifugal compressors by Wiesner [Wiesner 1979], Casey and Strub: the results of these investigations differ from Author to Author, as do their respective conclusions, but one common point all agreed upon is the definition of a reference Reynolds number based on the width of the exit section:

$$\text{Re} = \frac{\mathbf{U}\_2 \mathbf{b}\_2}{\nu} \tag{4}$$

By contrast, since we are interested here in introducing correction factors to the Balje charts, it was necessary to adopt the same choice of parameters: therefore, in this work the *Re* definition as reported in [Balje 1981] has been used throughout:

$$\text{Re} = \frac{\mathbf{U}\_2 \mathbf{D}\_2}{\nu} \tag{5}$$

Some scaling formulations include the influence of Reynolds number and surface roughness, but in this work we consider only hydraulically smooth surfaces, eliminating thus the roughness variable from the picture, also in consideration of the rather scant data available on the few prototypal rotors in the ultra-micro scale range. The derivation of a "universal" formula is intrinsically difficult, due to the substantial difference in the flow phenomenology, so that each class of machines requires a specific analysis. The objective of this work is to propose a preliminary method to scale the efficiency of ultra-microcompressors and turbines, investigating the possibility to extend the applicability of Balje charts for miniaturized machines, to reduce design time- and resources investment.

### **3.1 Reynolds number effects – Problem formulation and coefficient definition**

The general functional relationship proposed in the available references is of the so-called Stodola form:

$$\frac{1-\eta}{1-\eta\_{\text{ref}}} = \mathbf{a} + (1-\mathbf{a}) \left[\frac{\text{Re}\_{\text{ref}}}{\text{Re}}\right]^n \tag{6}$$

Whereas the coefficients *a* and *n* differ from Author to Author, as represented in Table 1.

Ultra Micro Gas Turbines 11

Notice that Equations (6) and (7) appear to be "complex" enough (i.e., to subsume a deep enough phenomenological model) to yield a good estimate of the losses for a particular class of machines such as the ultra-micro ones considered here. To circumvent the lack of a large experimental database, we decided to follow a different "type" of empirical experiments, in which numerical simulations substitute for laboratory tests. A sufficiently large set of data was created by means of accurate numerical simulations, and values for the constants a, k and k' in equations 6 and 7 above were obtained by a best fit procedure. Thus [Capata &

The coefficients in equation (8) provide a good agreement with the values reported in literature, particularly with the model by Wiesner. An direct confirmation of the validity of our procedure was obtained by applying equation (8) to compute the efficiency of an ultramicro compressor designed by the research group at MIT. Finally we suggest to adopt a polytropic efficiency within 0.55 and 0.7 in the preliminary design of the turbomachines.

> p p 2 1c = β

<sup>k</sup> T T 2 1c

t

β

where p1 is the inlet static pressure equal to 1 atm, p2 is the compressor outlet static pressure, T1 and T2 the temperatures of beginning and end compression process respectively, and T3, T4 refer to the turbine expansion. The compression ratio βc = 2 is different from the expansion ratio βt = 1.94, due to the combustor losses (approximately 3%). Once that the static temperatures in the main points of the cycle are known, it is possible to evaluate the mixture ratio α and the equivalent ratioφ. Then, the compression work *Wc* the

2

T c p T

4

T t p T

3

T p T

air 1

mix 3

mix 2

<sup>=</sup>

4 3

expansion one *Wt* and combustion process *Q,* can be calculated:

<sup>1</sup> T T

c c p k 1

η β

> ( ) <sup>t</sup> <sup>p</sup> <sup>t</sup> k 1 k

−

η

−

0.25 Reref 0.084 Re ref

<sup>⋅</sup> <sup>−</sup> =+⋅ <sup>−</sup> (8)

(9)

(11)

= (10)

W c dT <sup>=</sup> (12)

W c dT <sup>=</sup> (13)

Q c dT <sup>=</sup> (14)

Sciubba 2007] the final formula we propose for the scale-down is:

ref

η

**3.2 The thermodynamic CYCLE – General overview** 

The cycle equation sets are:

η

<sup>1</sup> Re 0.50 0.50 1 Re


Table 1. Summary of the most popular efficiency correction equations

Where the coefficient *a* represents the Reynolds number independent loss fraction, but it is in fact sometimes itself a function of *Re*, and the exponent *n*, as proposed in Strub [Strub 1987], is in general taken to be inversely proportional to the Reynolds number: this approach accounts for the decreasing influence of the viscous losses for high values of *Re*. The main shortcomings of this approach are:


$$\mathbf{n} = \mathbf{k}' \left( \frac{1}{\mathrm{Re/Re}\_{\mathrm{ref}}} \right)^k \tag{7}$$

1925 Moody 0.25 0.75 0.33 Propeller turbines 1930 Ackeret & Muhlemann 0.50 0.50 0.20 Hydraulic turbines

1951 Davis, Kottas & Moody 0.00 1.00 variable All turbomachines 1954 Hutton 0.30 0.70 0.20 Kaplan turbines

1961 O'Neil & Wickli 0.00 1.00 variable Radial compressors

1971 Mashimo et Al. 0.25 min 0.75 max 0.20 Radial compressors 1974 Mashimo et Al. 0.15-0.57 0.43-0.85 0.20-0.50 Radial compressors 2007 Capata, Sciubba & Silva 0.50 0.50 0.25 All turbomachines

Where the coefficient *a* represents the Reynolds number independent loss fraction, but it is in fact sometimes itself a function of *Re*, and the exponent *n*, as proposed in Strub [Strub 1987], is in general taken to be inversely proportional to the Reynolds number: this approach accounts for the decreasing influence of the viscous losses for high values of *Re*. The main

• The coefficient *a* is likely to remain constant only in a small range of Reynolds

k

(7)

ref

Re Re <sup>=</sup> 

<sup>1</sup> n k'

• The Re-independent losses are also related to other factors like for example leakage; • It is also well known that *a* varies with both geometry and manufacturing techniques even for machines with the same *Re*. As a first approximation, we assumed that the manufacturing process and clearances fit with the parameters imposed for the Balje charts. This assumption is not far from reality, because the design of such small devices is strongly constrained by factors unrelated with fluid-dynamics, so that ultra-micromachines are indeed all quite similar to each other, and because the estimated clearances [Epstein 2003] are in the same range as those reported on the Balje charts. • The exponent *n* varies considerably from author to author and this might depend on the different intrinsic accuracy of the data used by different authors, originated by the neglection of the effects of relative roughness. As stated above, in this work we concentrate on the influence of the Reynolds number, thus as a first step we, too, neglected the relative roughness, especially because we could find no experimental data in the range of the geometrical scales of importance here. Wiesner [Turton 1984] pointed out that it is useful to introduce an explicit Re-dependence in this exponent,

*Viscositydependent loss fraction (1-a)* 

> 0.50 0.76

> 1.00 1.00

*Exponent*

0.10 0.20

0.20 0.10

*<sup>n</sup>Machine type* 

Radial compressors

Axial compressors Radial compressors

*Inviscid loss fraction"a"*

1942 Moody 0.00 1.00 0.20 Pumps 1947 Pfleiderer 0.00 1.00 0.10 Pumps

1958 Rotzoll 0.00 1.00 variable Pumps

0.50 0.24

0.00

Table 1. Summary of the most popular efficiency correction equations

and proposed a functional relation of the form:

*Year Source* 

<sup>1960</sup>Wiesner

Fauconnet

1965 ASME Code PTC-10 0.00

shortcomings of this approach are:

numbers;

Notice that Equations (6) and (7) appear to be "complex" enough (i.e., to subsume a deep enough phenomenological model) to yield a good estimate of the losses for a particular class of machines such as the ultra-micro ones considered here. To circumvent the lack of a large experimental database, we decided to follow a different "type" of empirical experiments, in which numerical simulations substitute for laboratory tests. A sufficiently large set of data was created by means of accurate numerical simulations, and values for the constants a, k and k' in equations 6 and 7 above were obtained by a best fit procedure. Thus [Capata & Sciubba 2007] the final formula we propose for the scale-down is:

$$\frac{1-\eta}{1-\eta\_{\text{ref}}} = 0.50 + 0.50 \cdot \left[\frac{\text{Re}\_{\text{ref}}}{\text{Re}}\right]^{0.084\left(\frac{\text{Re}\_{\text{ref}}}{\text{Re}}\right)^{0.25}}\tag{8}$$

The coefficients in equation (8) provide a good agreement with the values reported in literature, particularly with the model by Wiesner. An direct confirmation of the validity of our procedure was obtained by applying equation (8) to compute the efficiency of an ultramicro compressor designed by the research group at MIT. Finally we suggest to adopt a polytropic efficiency within 0.55 and 0.7 in the preliminary design of the turbomachines.

### **3.2 The thermodynamic CYCLE – General overview**

The cycle equation sets are:

$$\mathbf{p}\_2 = \mathbf{p}\_1 \boldsymbol{\beta}\_c \tag{9}$$

$$\mathbf{T\_2} = \mathbf{T\_1} \boldsymbol{\mathcal{B}}\_c^{\frac{\mathbf{k\_c} - 1}{\mathbf{k\_c} \boldsymbol{\eta\_p}}} \tag{10}$$

$$\mathbf{T\_4} = \mathbf{T\_3} \left(\frac{\mathbf{1}}{\mathcal{B}\_t}\right)^{\frac{(\mathbf{k}\_t - 1)}{\mathbf{k}\_t}\eta\_\mathbf{p}} \tag{11}$$

where p1 is the inlet static pressure equal to 1 atm, p2 is the compressor outlet static pressure, T1 and T2 the temperatures of beginning and end compression process respectively, and T3, T4 refer to the turbine expansion. The compression ratio βc = 2 is different from the expansion ratio βt = 1.94, due to the combustor losses (approximately 3%). Once that the static temperatures in the main points of the cycle are known, it is possible to evaluate the mixture ratio α and the equivalent ratioφ. Then, the compression work *Wc* the expansion one *Wt* and combustion process *Q,* can be calculated:

$$\mathbf{W}\_{\mathbf{c}} = \int\_{\mathbf{r}\_1}^{\mathbf{r}\_2} \mathbf{c}\_{p\_{\text{air}}} \, \text{d}\mathbf{T} \tag{12}$$

$$\mathbf{W}\_{\rm t} = \int\_{\rm r\_3}^{\rm r\_4} \mathbf{c}\_{p\_{\rm mix}} \, \mathbf{d} \, \mathbf{T} \tag{13}$$

$$\mathbf{Q} = \int\_{T\_2}^{T\_3} \mathbf{c}\_{p\_{\rm mix}} \, \mathbf{d} \, \mathbf{T} \tag{14}$$

Ultra Micro Gas Turbines 13

continues steps in the development of such manufacturing techniques has been recognized and more complex 3-D geometries can be, nowadays, produced. An other design constraints are the maximum obtainable blades heights. This value, with the laser techniques, was limited to 500 µm few years ago, but now it is possible to obtain higher values, clearly, with greater costs. The Reynolds number is lower than conventional machines and considering the several constructive limits, will be difficult to succeed to create a geometry to avoiding separation, moreover the net output power will be probably lower than the hypothetical one with simple scale considerations. The work will be, substantially, produced by the mass forces. The conventional radial machines, usually, are equipped with inducer or exducer and, guided through sweet bending of the channels through the rotor, in such way to guarantee the lower possible losses for the interaction between boundary layer and angles or the flow separation: in this case it could not be constructively simple or favourable economically to realize a rounded inlet manifold or an axial outlet channel. Considering the diffusive process of the compressor, it could be useful to increase the chord length and to compensate the absence of constriction in the channel, increasing the blade thickness, in particular the trailing edge will be thicker than conventional machine. Consequently, the more opportune choice could be the reduction of the gap between the rotor and the case, to decrease the ventilation losses, but to minimize such distance implies to increase the resistance losses for the low blade height. Recent studies of the MIT have evidenced that a good strategy to such scale is to realize a gap equal approximately to 1% of the blade height. The problem of the flow separation in turbine is less problematic than in the compressor. The Reynolds number value is about 104 or lower, due to the elevated temperatures produced by the combustion. The significant losses will be at the flow exit, due to the straight angle (90°)

and of the swirl residual. To partially recover this residual a diffuser will be insert.

Undoubtedly, the combustion chamber plays a crucial role in the design of the entire device, considering, above all, the necessity to limit the dimensions. The main requirements of a combustor are high efficiency, low pressure drops, high structural resistance and low emissions. Surely, for a conventional combustor is simpler to obtain these requirements, thanks to the ability to realize - to the macro scales - complex structures. In favour of a micro combustor there is an higher energy density, coupled to a greater elaborated flow rate for

In a UMGT, the relative volume, will be, approximately, 40 times greater than a traditional system. The largeness of the combustion chamber, in fact, is dictated by the necessity to completely develop the reactions and by the residence time, that it is the sum of the necessary time to the mixing (that scales with the dimensions of the device) and the chemical reaction time (that is fixed and forces to consider greater volumes at the micro scales). In a conventional engine, beyond 90% of the residence time is reserved to the mixing. At this point it is useful to introduce the number of Damkohler "Da", that it is the ratio between the fluid dynamic time, (how much time the fluid spends to cross the combustion chamber) and the chemical reaction time. Experimentally it is verified that, for having a complete reaction, it is necessary to have Da number higher the one (Da > 1). In a combustor is fundamental to obtain the highest possible energy density, and to achieve this objective, is necessary to be capable to maintain high flow rate for volume unit. Moreover is necessary to avoid to increase the chamber dimensions. At the same time it is fundamental

**4.1 Combustion chamber at MIT** 

volume unit, as can be noticed in table 2.

remembering that the molar fractions (necessary to calculate the pmix c ) are obtained from the equivalence ratio:

$$\frac{\mathbf{n}\_{\text{C}\_{n}\text{H}\_{m}}}{\mathbf{n}\_{\text{air}}} = \phi \left( \frac{\mathbf{n}\_{\text{C}\_{n}\text{H}\_{m}}}{\mathbf{n}\_{\text{air}}} \right)\_{\text{stack}} \tag{15}$$

$$\mathbf{x}\_{\mathbf{C}\_{n}\mathbb{H}\_{n}} = \frac{\mathbf{n}\_{\mathbf{C}\_{n}\mathbb{H}\_{m}}}{\mathbf{n}\_{\mathbf{C}\_{n}\mathbb{H}\_{m}} + \mathbf{n}\_{\text{air}}} \tag{16}$$

$$\mathbf{x}\_{\text{air}} = \mathbf{1} - \mathbf{x}\_{\text{C}\_{n}\text{H}\_{m}} \tag{17}$$

Once defined the net work *Wu*, it is possible to determine the actual thermodynamic efficiency *ηth* :

$$
\eta\_{\rm th} = \frac{\mathcal{W}\_u}{\mathcal{Q}} \tag{18}
$$

The net power can be calculated as follows:

$$\mathbf{P} = \eta\_c \dot{\mathbf{m}}\_{\text{air}} \left[ \left( \mathbf{1} + \frac{\mathbf{1}}{\alpha} \right) \eta\_m \mathbf{L}\_{\text{t}} - \frac{\mathbf{L}\_{\text{c}}}{\eta\_m} \right] \tag{19}$$

$$
\dot{\mathbf{m}}\_{\text{C}\_{\text{n}}\text{H}\_{\text{m}}} = \frac{\dot{\mathbf{m}}\_{\text{air}}}{\alpha} \tag{20}
$$

And the global efficiency ηg is:

$$
\eta\_{\ell} = \frac{\text{P}}{\text{LHV} \cdot \dot{\text{m}}\_{\text{fuel}}} \tag{21}
$$

### **4. UMGT component analysis**

The first goal in the design of an UMGT is to contain the device overall dimensions and to avoid, if possible, a multi stage configuration: wanting to obtain a reasonable compression ratios, the choice falls on radial machine (centrifugal compressor and centripetal turbine). Being the thermodynamics invariant regarding the macro turbines, to generate the required specific power with single stage machines, it will be, however, necessary to adopt compression ratios between 2:1 and 4:1 and TIT within 1200 - 1600 K. Higher temperatures has to be avoided, due to the difficulty to integrate a cooling system. The centrifugal stresses (most important), as the specific work, depends on the square of the speed, that implies for, the considered values of U (velocity), between 300 and 600 m/s, stresses in the order of the hundreds of MPa. Not being able to take advantage of the conventional turbomachines manufacturing techniques and considering the various fluid dynamic problematic at the micro scales, it will be necessary to study which parameters of the conventional design are still adaptable and, where is necessary to act ex-novo in order to redefine an optimal area of design. The most important constrain in the design procedure is the adoption of 2-D extruded geometries for the blades, using the photolithography techniques, now widely diffuse for the production of MEMS (Micro Electro-Mechanical-Systems). Fortunately

remembering that the molar fractions (necessary to calculate the pmix c ) are obtained from the

air air stech

n

n m C H

Once defined the net work *Wu*, it is possible to determine the actual thermodynamic

th

e air m t

<sup>1</sup> <sup>L</sup> Pm1 L

n m

C H <sup>m</sup> <sup>m</sup>

g

η

η

n m

C H air

u

 η

air

fuel

α

P LHV m

The first goal in the design of an UMGT is to contain the device overall dimensions and to avoid, if possible, a multi stage configuration: wanting to obtain a reasonable compression ratios, the choice falls on radial machine (centrifugal compressor and centripetal turbine). Being the thermodynamics invariant regarding the macro turbines, to generate the required specific power with single stage machines, it will be, however, necessary to adopt compression ratios between 2:1 and 4:1 and TIT within 1200 - 1600 K. Higher temperatures has to be avoided, due to the difficulty to integrate a cooling system. The centrifugal stresses (most important), as the specific work, depends on the square of the speed, that implies for, the considered values of U (velocity), between 300 and 600 m/s, stresses in the order of the hundreds of MPa. Not being able to take advantage of the conventional turbomachines manufacturing techniques and considering the various fluid dynamic problematic at the micro scales, it will be necessary to study which parameters of the conventional design are still adaptable and, where is necessary to act ex-novo in order to redefine an optimal area of design. The most important constrain in the design procedure is the adoption of 2-D extruded geometries for the blades, using the photolithography techniques, now widely diffuse for the production of MEMS (Micro Electro-Mechanical-Systems). Fortunately

α

= +−

W Q

 <sup>=</sup> 

(15)

n n <sup>=</sup> <sup>+</sup> (16)

air C Hn m x 1x = − (17)

= (18)

(19)

<sup>=</sup> (20)

<sup>=</sup> <sup>⋅</sup> (21)

c

m

 η

C Hn m C Hn m

n n n n φ

n n

C H

x

η

equivalence ratio:

efficiency *ηth* :

The net power can be calculated as follows:

And the global efficiency ηg is:

**4. UMGT component analysis** 

continues steps in the development of such manufacturing techniques has been recognized and more complex 3-D geometries can be, nowadays, produced. An other design constraints are the maximum obtainable blades heights. This value, with the laser techniques, was limited to 500 µm few years ago, but now it is possible to obtain higher values, clearly, with greater costs. The Reynolds number is lower than conventional machines and considering the several constructive limits, will be difficult to succeed to create a geometry to avoiding separation, moreover the net output power will be probably lower than the hypothetical one with simple scale considerations. The work will be, substantially, produced by the mass forces. The conventional radial machines, usually, are equipped with inducer or exducer and, guided through sweet bending of the channels through the rotor, in such way to guarantee the lower possible losses for the interaction between boundary layer and angles or the flow separation: in this case it could not be constructively simple or favourable economically to realize a rounded inlet manifold or an axial outlet channel. Considering the diffusive process of the compressor, it could be useful to increase the chord length and to compensate the absence of constriction in the channel, increasing the blade thickness, in particular the trailing edge will be thicker than conventional machine. Consequently, the more opportune choice could be the reduction of the gap between the rotor and the case, to decrease the ventilation losses, but to minimize such distance implies to increase the resistance losses for the low blade height. Recent studies of the MIT have evidenced that a good strategy to such scale is to realize a gap equal approximately to 1% of the blade height. The problem of the flow separation in turbine is less problematic than in the compressor. The Reynolds number value is about 104 or lower, due to the elevated temperatures produced by the combustion. The significant losses will be at the flow exit, due to the straight angle (90°) and of the swirl residual. To partially recover this residual a diffuser will be insert.

### **4.1 Combustion chamber at MIT**

Undoubtedly, the combustion chamber plays a crucial role in the design of the entire device, considering, above all, the necessity to limit the dimensions. The main requirements of a combustor are high efficiency, low pressure drops, high structural resistance and low emissions. Surely, for a conventional combustor is simpler to obtain these requirements, thanks to the ability to realize - to the macro scales - complex structures. In favour of a micro combustor there is an higher energy density, coupled to a greater elaborated flow rate for volume unit, as can be noticed in table 2.

In a UMGT, the relative volume, will be, approximately, 40 times greater than a traditional system. The largeness of the combustion chamber, in fact, is dictated by the necessity to completely develop the reactions and by the residence time, that it is the sum of the necessary time to the mixing (that scales with the dimensions of the device) and the chemical reaction time (that is fixed and forces to consider greater volumes at the micro scales). In a conventional engine, beyond 90% of the residence time is reserved to the mixing. At this point it is useful to introduce the number of Damkohler "Da", that it is the ratio between the fluid dynamic time, (how much time the fluid spends to cross the combustion chamber) and the chemical reaction time. Experimentally it is verified that, for having a complete reaction, it is necessary to have Da number higher the one (Da > 1). In a combustor is fundamental to obtain the highest possible energy density, and to achieve this objective, is necessary to be capable to maintain high flow rate for volume unit. Moreover is necessary to avoid to increase the chamber dimensions. At the same time it is fundamental

Ultra Micro Gas Turbines 15

the device. The relative technologies to the photolithography are extremely favourable for the injectors manufacturing. The choice of the materials represents an other design crucial point; the silicon introduces serious problems of plastic deformation at 950 K. A combustor with a dilution zone (for cooling the flow) can be adopted, and materials like silicon carbide SiC presents an higher thermal resistances. Remember that the thermal fluxes, previously discussed, facilitate the walls cooling. The dilution ("Dual zones") extends the range of the elaborated flow rate, but at the same time decreases the obtainable maximum efficiency of 10- 20%. These combustors have been tested with an outlet temperatures of 1800 K approximately.

Fig. 4. Combustion efficiency of an hydrogen micro combustor [Peirs 2003, Epstein 1997, 2003]

The necessity to assure the flame stability introduces more difficulties, so the configuration with dilution zone facilitates the recirculation in the primary zone through the air that enters in the secondary zone. Moreover the mixture ratio (in this case close to the steichiometric one) allows to decrease the reaction times. The adoption of the slots increases the turbulent phenomena in the chamber. Other fuel (as ethylene, propane, butane, methane, ecc) and other configurations (with platinum catalysts) have been tested and all the data are collected in Figure 5 figure according to the Damkohler number. It is evidenced how it is necessary to work with Damkohler numbers at least equal to 2, to obtain good combustion efficiency.

Fig. 5. Combustion efficiency to varying the Damkohler number


(note: the residence times are calculated using inlet pressure and an average flow temperature of 1000 K)

Table 2. Comparison between a conventional combustor and a micro combustor [MIT prototype – Epstein 2003]

to maintain the Damkohler number higher than the unit. It can act in two ways: increase the fluid dynamic time to complete the combustion or decrease the necessary residence times. Clearly, the first choice contrasts with requirement of maximum energy density, since previews the greater dimensions, while, the second one, is applicable with good result by the use of catalysts. The greater surface/volume ratio of a micro combustor increases the efficiency of catalysts, accelerating the chemical reactions. In this case the heat losses are not negligible, as well as in the traditional systems, since an overall efficiency and reaction temperature reduction have been produced. In effects it has been demonstrated that the relationship between lost heat and generated heat is inversely proportional to the inverse of the hydraulic diameter of the combustion chamber:

$$\frac{\mathbf{Q}\_{\text{los}}}{\mathbf{Q}\_{\text{prod}}} \approx \frac{1}{\mathbf{D}\_{\text{hyd}}^{-1^2}}\tag{22}$$

The hydraulic diameter of a micro combustor is of the order of millimetre, one hundred times lower than conventional one. This fact implies that the heat losses correlated to the heat produced by the combustion will be approximately one hundred times higher than the traditional combustors. For these reasons will be improbable to achieve an efficiency of 99% compared to the commercial systems. Finally, a reaction temperature drop increases the reaction time. All these factors reduce the available "design space", as consequence of an important decrease of the Damkohler number, and the flammability range, due to the reaction time decrease. Clearly the choice of fuel completely modifies the design limits and, maybe, the conditions will be more restrictive. An effective way to reduce the residence times is the insertion of a premixing device, for example immediately after the compressor exit, after the "flame holder", so that the mixture reaches the combustor very stirred: this can produce backfire problems and instability, but the residence time is reduced of a factor 10 regarding conventional 5-10 ms. A method to reduce the heat losses and, at the same time, to cool the combustor walls consists in leading the compressor outlet air around to the external wall of the chamber. This technique derived directly from the conventional inverse flow combustor, the only difference is that the liner is cooled for conduction rather than through a fluid film. The configuration with premixing device previews the fuel injection before the chamber inlet, to begin the mixing with the air and to reduce the dimensions of

(note: the residence times are calculated using inlet pressure and an average flow temperature of 1000 K) Table 2. Comparison between a conventional combustor and a micro combustor [MIT

to maintain the Damkohler number higher than the unit. It can act in two ways: increase the fluid dynamic time to complete the combustion or decrease the necessary residence times. Clearly, the first choice contrasts with requirement of maximum energy density, since previews the greater dimensions, while, the second one, is applicable with good result by the use of catalysts. The greater surface/volume ratio of a micro combustor increases the efficiency of catalysts, accelerating the chemical reactions. In this case the heat losses are not negligible, as well as in the traditional systems, since an overall efficiency and reaction temperature reduction have been produced. In effects it has been demonstrated that the relationship between lost heat and generated heat is inversely proportional to the inverse of

lost

prod hyd Q 1

The hydraulic diameter of a micro combustor is of the order of millimetre, one hundred times lower than conventional one. This fact implies that the heat losses correlated to the heat produced by the combustion will be approximately one hundred times higher than the traditional combustors. For these reasons will be improbable to achieve an efficiency of 99% compared to the commercial systems. Finally, a reaction temperature drop increases the reaction time. All these factors reduce the available "design space", as consequence of an important decrease of the Damkohler number, and the flammability range, due to the reaction time decrease. Clearly the choice of fuel completely modifies the design limits and, maybe, the conditions will be more restrictive. An effective way to reduce the residence times is the insertion of a premixing device, for example immediately after the compressor exit, after the "flame holder", so that the mixture reaches the combustor very stirred: this can produce backfire problems and instability, but the residence time is reduced of a factor 10 regarding conventional 5-10 ms. A method to reduce the heat losses and, at the same time, to cool the combustor walls consists in leading the compressor outlet air around to the external wall of the chamber. This technique derived directly from the conventional inverse flow combustor, the only difference is that the liner is cooled for conduction rather than through a fluid film. The configuration with premixing device previews the fuel injection before the chamber inlet, to begin the mixing with the air and to reduce the dimensions of

1.2

<sup>Q</sup> <sup>D</sup> <sup>∝</sup> (22)

prototype – Epstein 2003]

the hydraulic diameter of the combustion chamber:

**Length** 0.2 m 0.001 m **Volume** 0.073 m3 6.6 10-8 m3 **Cross-sectional area** 0.36 m2 6 10-5 m2 **Inlet total pressure** 37.5 atm 4 atm **Inlet total temperature** 870 K 500 K **Mass flow rate** 140 kg/s 1.8 10-4 kg/s **Residence time** 7 ms 5 ms **Efficiency** > 99% > 0.9 **Pressure ratio** > 0.95 > 0.95 **Exit temperature** 1800 K 1600 K **Power density** 1960 MW/m3 3000 MW/m3

**Conventional Combustor Micro combustor** 

the device. The relative technologies to the photolithography are extremely favourable for the injectors manufacturing. The choice of the materials represents an other design crucial point; the silicon introduces serious problems of plastic deformation at 950 K. A combustor with a dilution zone (for cooling the flow) can be adopted, and materials like silicon carbide SiC presents an higher thermal resistances. Remember that the thermal fluxes, previously discussed, facilitate the walls cooling. The dilution ("Dual zones") extends the range of the elaborated flow rate, but at the same time decreases the obtainable maximum efficiency of 10- 20%. These combustors have been tested with an outlet temperatures of 1800 K approximately.

Fig. 4. Combustion efficiency of an hydrogen micro combustor [Peirs 2003, Epstein 1997, 2003]

Fig. 5. Combustion efficiency to varying the Damkohler number

The necessity to assure the flame stability introduces more difficulties, so the configuration with dilution zone facilitates the recirculation in the primary zone through the air that enters in the secondary zone. Moreover the mixture ratio (in this case close to the steichiometric one) allows to decrease the reaction times. The adoption of the slots increases the turbulent phenomena in the chamber. Other fuel (as ethylene, propane, butane, methane, ecc) and other configurations (with platinum catalysts) have been tested and all the data are collected in Figure 5 figure according to the Damkohler number. It is evidenced how it is necessary to work with Damkohler numbers at least equal to 2, to obtain good combustion efficiency.

Ultra Micro Gas Turbines 17

micron. It is therefore from is easy to verify as the great part of the design development is dedicated to the bearings and to the rotor dynamics. The first reflection is, due to the high rotational speed (> 20000 rad/s), the device will work in supercritical conditions, with operational frequencies higher than the resonance ones and for this reason the study of the stability will be primary in the machine design. Clearly the bearings play a dominant role in the rotor dynamics as they must support axial and radial thrust of the rotor, dampen the oscillations and support the forces deriving by the accelerations of the rotary parts, without to count the electric forces and the operational pressures. It cannot certainly be neglected that the supports must be able to supporting the high turbine temperatures and the thermal gradient presents and, then, be able to work in any operational condition. At last the resolution of all these problems must be consider the actual technological limitations. Other devices MEMS with rotary parts currently exist, but the angular velocities are such to allow to using not-lubricated bearings. Moreover do not exist in commerce such "little bearings" to be used for these rotors. Honestly, we have to mentioned two manufacturers that guarantee dry bearings at 200000 rpm (20933 rad/s). Therefore, the academic study focuses on two possible solutions: electromagnetic or air bearings. The first solution introduces the possibility to take advantage of magnetic fields or electrical ones to support the rotors loads. The problem relatively to the magnetic fields resides in the impossibility to adopt ferromagnetic materials in the productive technologies chosen (recording laser and photolithography), moreover the Curie point is such configuration not to allow of using these systems to the temperatures previewed in turbine and would be therefore necessary to introduce a cooling system, with all the design constraints and possibilities connected. Studies have been carried on the electric fields, but the forces that are succeeded to produce are decidedly inferior to support the considered loads. To all these consideration we must add that the electromagnetic bearings are strongly unstable and required a feedback control systems, which would complicate the installation. The air bearings introduce numerous advantages, in particular in terms of constructive simplicity, of loads capability, and relative insensibility to the problem of the high temperatures. Currently these device are already used for medium-small dimensions turbomachines. At smaller scales the gas bearings are wide used in micro gyroscopic system since many years. Wanting to make scale considerations it can be said that, to parity of load conditions, the ability of these bearings grows up with the overall dimensions decrease, because the ratio volume/surface decreases and consequently the inertial load. Certainly the rotor dynamics results to be, partially, simpler (the introduced structure is more rigid, if compared to the conventional ones), thus allowing the approximation of the rigid body. The development of the bearings has to preview two different use: first, the bearings must support the radial loads, second, must support the axial loads. These bearings are composed from a cylindrical hinge in contact with a lubricating support. More efficient models exist, but considering the complexity of the system, the more reasonable choice is the first one. The lubricating fluid in our case is air in pressure and according to how it is injected, the bearings are distinguished in "hydrostatic" if the source is external and "hydrodynamic" if the support forces are directly generated by the spin of the disc (figure 8). Mixed configurations are possible (figure 9). Since the UMGT includes a compressor is possible to adopt both the configurations, and both solution are able to satisfying the loads requirements and temperatures stresses to these dimensions. The two types of bearings are characterized by various dynamic characteristics. In the hydrodynamic bearings the load ability grows up to increasing of the rotational speed, because the pressure of the film between disc and support increases with the spin. In theory, also for a hydrostatic bearing a mechanism of this type can be fed; we
