W L Wei

K Mahdjoubi
email: kouroch.mahdjoubi@univ-rennes1.fr

C Brousseau

O Emile

A Sharaiha

Enhancement of Directivity of an OAM Antenna by Using Fabry-Perot Cavity

Keywords: orbital angular momentum, Fabry-Perot cavity, circular antenna array, patch antenna. I

The circular phased antenna array is a common way to generate waves bearing Orbital Angular Momentum (OAM) in the radio frequency band, but the directivity of this antenna is relatively low. To overcome this drawback, in this paper, we use a Fabry-Perot cavity to enhance the directivity of an OAM antenna based on a circular phased array of patch antennas. The Fabry-Perot cavity consists of a ground plane, an air cavity and a partially reflecting surface (PRS) made of metallic strips. Simulation results show that the OAM antenna achieves a directivity of 16.2 dB with an enhancement of 9.2 dB in E and H planes.

INTRODUCTION

Orbital angular momentum (OAM) has been proposed to improve spectral efficiency [START_REF] Mohammadi | Orbital angular momentum in radio -a system study[END_REF][START_REF] Tamburini | Encoding many channels on the same frequency through radio vorticity: first experimental test[END_REF][START_REF] Wang | Terabit free-space data transmission employing orbital angular momentum multiplexing[END_REF][START_REF] Yan | High-capacity millimetre-wave communications with orbital angular momentum multiplexing[END_REF] in radio communications, by creating multiple sub-channels of propagation corresponding to the twisting degree of the electromagnetic wave.

Whereas the phase of a usual plane wave is constant on the wave front, the phase α of OAM waves undergoes a linear variation along the angular coordinate  (roll angle): α = l, where l is an integer called the "topological charge" or the order of the OAM mode.

In the radio frequency band, a circular phased array is a common technique for generating OAM waves [START_REF] Mohammadi | Orbital angular momentum in radio -a system study[END_REF][START_REF] Thidé | Utilization of photon orbital angular momentum in the low-frequency radio domain[END_REF]. It is generally composed of N antennas, where each one is fed by the same signal with a ±2πl/N phase shift compared to its neighbor. Some practical constructions are proposed in [START_REF] Bai | Experimental circular phased array for generating OAM radio beams[END_REF][START_REF] Wei | Generation of OAM waves with circular phase shifter and array of patch antennas[END_REF][START_REF] Tennant | Generation of OAM radio waves using circular time-switched array antenna[END_REF].

In this paper, we present a method to enhance the directivity of an OAM antenna by using the Fabry-Perot (FP) cavity. A circular phased array of four patch antennas is used to generate waves bearing an OAM mode l = 1. This OAMwave generator is embedded inside the FP cavity and works at a frequency of 2.5 GHz.

II. MODEL OF FABRY-PEROT CAVITY

The model of the FP cavity is shown in Fig. 1. It is composed of a ground plane which eliminates the back radiation, a primary source (patch antenna) and a partially reflecting surface (PRS). When the internal wave rays emitted by the primary source arrive at the upper PRS, they are partially reflected back to the cavity and partially transmitted out. Then, when the reflected rays arrive at the bottom ground plane, they are reflected again towards the cavity. Here we use a PEC ground plane and suppose that the rays are totally reflected at this surface.

To obtain a maximal directivity, the transmitted rays should all be in phase so that they can make a constructive interference. According to [START_REF] Mahdjoubi | An overview on the design and properties of EBG antennas[END_REF], the thickness of the FP cavity should meet the following requirement:

     0 21 4 cos c Dn f        
where c is the speed of the light in free space, f0 is the working frequency, β is the phase of the reflection coefficient of the PRS, n is an integer corresponding to the cavity mode number, θ is the incidence angle of the rays (see Fig. 1).

A. Phased Patch Array

Here we intend to use a circular phased array of patch antennas to generate the OAM wave [START_REF] Wei | Generation of OAM waves with circular phase shifter and array of patch antennas[END_REF]. For creating an OAM mode l = 1 with N = 4 antennas, the phase step between each element should be 2πl/N = π/2 radians = 90°. The configuration of the OAM antenna is shown in Fig. 2. The length and width of single patch antenna are 36.5 and 27.4 mm, respectively. The patch array is manufactured on a FR4 substrate with a thickness of 1.6 mm and a relative permittivity of 4.4. All the patch antennas are probe fed using the same signal but with an incremental phase shift between each patch. Fig. 3 presents the reflection coefficient of a single patch antenna, we can see that it is well matched around 2.5 GHz. When the radius of the patch array is 50 mm, the magnitude and phase patterns of the generated wave, observed on a circular area with a radius of 150 mm lying 50 mm above the patch array, are presented in Fig. 4 for the main polarization Ex (see Fig. 2). We can observe that the magnitude at the centre is much smaller than the surroundings and the phase rotates around the centre with a 2π phase shift in one turn. This shows indeed that both the amplitude and the phase of the generated wave correspond to a wave bearing an OAM mode l = 1. To show the influences of the array radius on the antenna directivity, Fig. 4 presents the E-plane radiation patterns with different array radiuses of 50, 80 and 110 mm. It can be observed that the OAM waves become more directive as the array radius increases, but naturally some side lobes appear. When the array radius keeps increasing, the side lobe becomes even comparable with the main lobe, which means a strong loss of energy.

B. Phased Patch Array in Fabry-Perot Cavity

It has been demonstrated that the FP cavity is able to enhance the directivity of an antenna [START_REF] Akalin | A highly directive dipole antenna embedded in a Fabry-Perot type cavity[END_REF][START_REF] Boutayeb | Directivity of an antenna embedded inside a Fabry-Perot cavity: Analysis and Design[END_REF]. Along this way, we would like to embed the OAM antenna inside the FP cavity to improve its directivity of the main lobe, as shown in Fig. 6. Because the OAM waves are more directive with a bigger array radius, here we choose an array radius of 110 mm.

To realize a good directivity, the wave rays need to be reflected enough times inside the FP cavity, therefore the dimension of the ground plane and the PRS should be large enough. In our design, the ground plane and the PRS both have a dimension of 600 mm × 600 mm. The PRS is made of a set of periodic metallic strips which are manufactured on a FR4 substrate with a thickness of 1.6 mm and a relative permittivity of 4.4. The period and width of the strips are 20 and 4 mm, respectively. According to (1), the cavity thickness depends on the working frequency, the phase of the reflection coefficient of the PRS and the incidence angle of the wave rays. From Fig. 5 we can see that when the array radius is 110 mm, the angle value corresponds to the maximum directivity is at ±15° for the main lobe, so the value of the incidence angle here is 15°. We simulated the PRS alone and found that the magnitude and phase of its reflection coefficient were respectively 0.944 and 0.9π. By substituting these values into (1), we can calculate that the thickness of the FP cavity for the cavity mode n = 0 is equal to 59 mm at a working frequency of 2.5 GHz.

We have varied the cavity thickness to optimize the antenna directivity, the results are shown in Table I. We can observe that the maximum directivity of the OAM antenna changes slightly with the cavity thickness, while the angle value corresponding to the maximum directivity maintains at 11°; the OAM antenna achieves a best directivity of 16.2 dB with a cavity thickness of 58 mm, which is the final value we have used. 15. 5 11 Fig. 7 presents the 3D radiation patterns of the patch antenna array (array radius equals to 110mm) with and without FP cavity. We can observe a null in the center which is one of the characteristics of the OAM waves. In addition, with the use of the FP cavity, the antenna directivity is enhanced and the side lobes are significantly suppressed at the same time.

To give a better view of the influence of the FP cavity on the OAM antenna directivity, we make a comparison of the Eplane radiation patterns in Fig. 8. It can be seen that with the use of the FP cavity, the antenna directivity increases in Eplane, from 7 to 16.2 dB. The maximum directivity is obtained for angle of 11°.

IV. CONCLUSIONS

In this paper, we have presented a method to enhance the directivity of an OAM antenna by embedding it inside a FP cavity. This OAM antenna is based on a 4-element circular phased patch array with an array radius of 110 mm and works at 2.5 GHz. Influences of the FP cavity thickness on the antenna directivity are studied. The OAM antenna finally achieves a directivity of 16.2 dB with an optimized cavity thickness of 58 mm.

Fig. 1 .

 1 Fig. 1. Model of the FP cavity with PRS

Fig. 2 .

 2 Fig. 2. Configuration of the OAM antenna

Fig. 3 .Fig. 4 .

 34 Fig. 3. Reflection coefficient of single patch antenna

Fig. 5 .

 5 Fig. 5. E-plane radiation patterns with different array radiuses

Fig. 6 .

 6 Fig. 6. Configuration of the OAM antenna & FP cavity

Fig. 7 .Fig. 8 .

 78 Fig. 7. 3D radiation patterns of the OAM antenna (array radius equals to 110mm): (a) without FP cavity; (b) with FP cacity

TABLE I

 I

	.	MAXIMUM DIRECTIVITY VALUE AND POSITION OF OAM
	ANTENNA WITH DIFFERENT CAVITY THICKNESSES
	Cavity Thickness (mm)	Max Directivity (dB)	Position (°)
	59		14.6	11
	58.5	15.7	11
	58		16.2	11
	57.5

ACKNOWLEDGMENT

The authors would like to thank China Scholarship Council (CSC) (No. 201306090101) for scholarship support.


Eric Ebert
email: eric.ebert@uni-rostock.de

Willfried Kröger

André Kleinwächter

Robert Kostbade

Karl Julius Weder

Nils Damaschke

HDNC -A Novel Technique for Cavitation Nuclei Characterization and Particle Count Concentration Measurements

Keywords:

Depicted is the Hydrodynamic Nuclei Concentration (HDNC) measurement technique. This technique is an interferometric particle characterization technique based on the Interferometric Particle Imaging (IPI) technique. Based on the laser light scattering of particles is the size of spherical bubbles estimated. A classification method provides information about the particle type.

In junction with the possibility to estimate the measurement volume is bubble size based particle count concentration estimated. The technique was applied on a ConRo ferry ship called "Amandine" travelling between Rotterdam and Dublin. Depicted are especially the fluctuations in the particle count concentration by bubble clouds in the wake of the ferry. Furthermore depicted is a new particle segmentation technique based on the particles phase information..

INTRODUCTION

Ca itatio i pai s the effi ie a d auses i atio s, e osio of a essel [ ]. The efo e a e a itatio p edi tio odels i po ta t fo the desig p o ess ut ot suffi ie t elia le at the o e t. Ship odel asi s a d a itatio ta ks a e e ui ed to p edi t the full s ale essels a itatio eha io .

The H d od a i Nu lei Co e t atio HDNC te h i ue

as du i g the Ko Ka p oje t de eloped. The HDNC te h i ue is a size ali atio f ee te h i ue a d o i es ode ate ha d a e a d alig e t effo t ith the a ilit to easu e u le size dist i utio s i the .. µ a ge a d u le ou t o e t atio s depe di g o the opti al o figu atio . The esti atio of the u lei spe t a is i the appli atio st o gl i flue ed the ofte ti es highe solid o e t atio o pa ed to the gas u le o e t atio i the I ish Sea. The efo e is the lassifi atio p o ess of the HDNC te h i ue esse tial fo a elia le a itatio u lei dist i utio statisti s.

METHODS

The HDNC technique is based on the scattering behavior of nuclei in a laser beam [START_REF] Kawaguchi | Size measurements of droplets and bubbles by advanced interferometric laser imaging technique[END_REF]. The illuminating laser beam from an inexpensive 532nm DPSS laser defines the dimension of the measurement volume in combination with an industrial camera with imaging optics. The usually applied scattering angle between the camera and the laser is 90 deg because of easy alignment and polarization invariance [START_REF] Ebert | Particle characterization system for industrial and naval applications[END_REF]. In case of the described full scale setup is a scattering angle of 81 deg applied because of the much higher available intensity. At this angle is the polarization of the laser beam important for the modulation depth of the signal. The laser had to be aligned correctly. Fig. 2 depicts the principle of measurement. Required are two optical accesses for the laser beam and the defocussed camera. The nuclei are depicted defocussed inside the focal length. The light waves with the origin at the glare points on the particles surface interfere with each at the imaging plane and provide interference pattern to the analysis.

The interference patterns are typical structured for different particle types. Homogenous spherical particles (like µm gas bubbles in water) have two dominant glare points at the specified scattering angle.

A fringe pattern occurs therefore in the imaging plane. The spacing between the fringes is proportional to the nuclei size. A calculation utilizing a Mie theory code provides the conversion factor between fringe count and particle size [START_REF] Ebert | Interferometric Particle Imaging for cavitation nuclei characterization in cavitation tunnels and in the wake flow[END_REF].

A particle with an inhomogeneous surface structure (like a solid in the water) has more than two dominant glare points on the surface. Therefore are speckle pattern visible in the imaging plane. Solid sizing algorithm is based on [START_REF] Ruiz | Feasibility of using glory and speckle patterns for sizing spherical and irregular particles[END_REF].

Bubble

Small Solid Large Solid Crystal After the acquisition of the nuclei images is a background subtraction required to become more accurate in particle segmentation and spectral analysis. The resulting in nuclei sizing and classification becomes therefore also more accurate. In a testing setup could be shown that the system noise is 0.56 µm (standard deviation in case of mono disperse drops).

Two nuclei detection algorithms based on template matching with a template in aperture shape are implemented. Usually a circular template like in fig. 4 The correlation by the template matching provides an image with local maxima at the position of the nuclei like in Fig. 6a). By a sine and cosine weighted template and a correlation for each of both is it possible to calculate the phase information for the particles image. This more sophisticated calculation method allows the detection of the nuclei center more accurate. Each point has therefore a value and a phase. This represents a vector for each pixel. In case of nuclei hits every vector the nuclei's center point. In other cases is no fix crossing point observable. By obtaining the count statistics of hitting vectors for each point is therefore a nuclei's centers detection possible. The higher accuracy is provided by a function fit through the vector hit count image. The local maximum of the fitted function provides the sub pixel accurate particle position. The phase information based method required much more complex calculations than the simple template matching method. Therefore is the analysis much slower. On a modern Intel i7 is the template matching possible with 10 to 15 frames per second with ~10 particles per image. The phase information based technique requires in the current implementation minutes per frame.

The applied classification of bubbles and solids relies on differences in the spectral characteristics (compare fig. 3). Fringe pattern have one sharp dominant peak in the PSD spectrum and speckle pattern have multiple minor peaks for each nuclei. Furthermore is the ratio of those peaks relevant. If the dominant peak is much higher than the second highest peak fringes will be observable. If more frequencies are mixed like in a speckle pattern the difference between highest and second highest peak becomes lower. The width of the peaks is a relevant quality criterion for the evaluation of the nuclei's interference pattern sharpness. With this information it's possible to classify into solids and bubbles.

A detection volume correction is necessary because of the Gaussian beam profile of the laser and the relation between particle size and scattered intensity (I ~ dp2) [START_REF] Albrecht | Laser Doppler and Phase Doppler Measurement Techniques[END_REF]. Therefore is the detection probability a function of the particle size. A correction method was implemented to overcome this issue [START_REF] Ebert | Interferometric Particle Imaging for cavitation nuclei characterization in cavitation tunnels and in the wake flow[END_REF].

The statistical analysis provides the information about the nuclei size distribution, the nuclei count concentration and the relation between bubble and solid count.

RESULTS AND DISCUSSION

In [START_REF] Ebert | Hydrodynamic Nuclei Concentration Technique in Cavitation Research and Comparison to Phase-Doppler Measurements[END_REF] is a comparison between the HDNC and the standard phase Doppler (PD) technique documented. Result of the comparison was that the HDNC is able to obtain similar quality nuclei size and count concentration results in much shorter measurement time for low concentration applications. A further improvement is the much lower hardware and calibration effort.

Therefore was the HDNC technique chosen during the KonKav project for full scale onboard measurements on the ConRo ferry ship "Amandine" and was applied at different ship model basins and cavitation tunnels (K15A, HYKAT, K22 and K21).

The full scale measurement is applied at 81 deg scattering angle because of limitations in the mechanical and optical accessibility [START_REF] Kleinwächter | Concept for optical full-scale measurements on ship propeller inflow and bubble size distribution[END_REF]. Two port holes above the propeller allow the alignment of the laser and the camera in the correct position and define the measurement volume in front of the propeller to observe the inflow. Fig. 8 Nuclei bursts occur approx. every 10 seconds with different particle count concentration intensities. Fig. 9 depicts the count concentration curve for a video recorded in the Celtic Sea. Therefore is the corrected nuclei count concentration not constant.

The nuclei bursts found in the wake flow of the Amandine are a significant difference between the model testing facilities and the full scale investigation. Usually is the goal for testing facilities to reach almost constant flow and pressure conditions during the tests. In the reality are those constant flow conditions not available also in the sense of nuclei count concentration. Between the lowest and highest nuclei count concentration is a factor of 10. Also the solid concentration was not constant in the Celtic sea during the measurement period of 42s.

The solids count is in mean around 9.17 times larger than the bubble count and has also large variations (5..40 per frame) during the measurements in the Celtic Sea.

CONCLUSION

The HDNC technique allows cavitation nuclei characterization measurements in different and also harsh environments like a ferry ship. The spectral classification method allows the separation of nuclei from solid particles. The developed segmentation techniques allow fast or more precise localizations of the particles. The nuclei size and count concentration can be estimated. A measurement of the particle concentration variation below a full scale ship was depicted.

Figure 1 .

 1 Figure 1. A bubble expanding at propellers surface recorded with a high speed camera and stroboscopic illumination The ate ualit has a i po ta t i flue e fo the a itatio i eptio [ ] & [ ]. The efo e u lei ou t o e t atio a d the u lei size dist i utio i the essels ake flo affe ts the a itatio eha io . Fo e a ple a e

Figure 2 .

 2 Figure 2. Principle of the HDNC technique[START_REF] Ebert | Hydrodynamic Nuclei Concentration Technique in Cavitation Research and Comparison to Phase-Doppler Measurements[END_REF]

Figure 3 .

 3 Figure 3. Interference pattern of different particle types

  a depicted is correlated with the nuclei image fig 4 b. a) b)

Figure 4 .

 4 Figure 4. a) Template image in aperture shape b) Nuclei interference pattern image[START_REF] Weder | Kreislokalisierung mit harmonischen Ortsfiltern für die HDNC-Partikeldetektion[END_REF]

Figure 5 .

 5 Figure 5. Analysis Flow of the HDNC technique[START_REF] Ebert | Hydrodynamic Nuclei Concentration Technique in Cavitation Research and Comparison to Phase-Doppler Measurements[END_REF]

Figure 6 .

 6 Figure 6. a) Correlation result from template matching b) Phase information[START_REF] Weder | Kreislokalisierung mit harmonischen Ortsfiltern für die HDNC-Partikeldetektion[END_REF]

Figure 7 .

 7 Figure 7. Two crossing vectors (red, blue) from the phaseInformation[START_REF] Weder | Kreislokalisierung mit harmonischen Ortsfiltern für die HDNC-Partikeldetektion[END_REF]

Figure 8 .

 8 Applied measurement hardware on the "Amandine" mounted on a linear and rotary stage to the porthole a) Laser head b) Camera and optics

Figure 9 .

 9 Figure 9. Measurement sample of 42 seconds recorded in the Celtic Sea (green min, mean and max lines for nuclei)T h e p a t i l e s i z e d i s t i u t i o a d t h e o e s p o d i g pa ti le ou t o e t atio dist i utio a e depi ted o fig .The ost easu ed pa ti les a e i the a ge et ee to µ . This at hes the a ge that a e fou d i lite atu e fo a itatio u lei sizes[START_REF] Carlton | Marine Propel lers and Propulsion Second Edition[END_REF].

Figure 10 .

 10 Figure 10. Particle size and particle count concentration distribution for the measurement on the "Amandine" with error bars.

ACKNOWLEDGMENTS

The authors thank the German Federal Ministry of Economics and Technology (BMWi) (grant number 03SX316D) and the project partners for the support of the KonKav-project.


Luca Mangani
email: luca.mangani@hslu.ch

Wolfgang Sanz

ISROMAC Marwan Darwish

Comparing the performance and accuracy of a pressure based and a density-based coupled solver

Keywords:

The velocity-pressure-density coupling algorithms that are at the core of computational fluid dynamics (CFD) methods can be grouped into two distinct groups: pressure-based and density-based methods. Pressure-based methods were originally developed for incompressible flows but have since been extended to address a wide range of flow conditions including compressible all speed flows. They are nowadays used in most commercial CFD codes both in their segregated and coupled form. Density-based methods, on the other hand, originated in the aeronautics industry for the simulation of compressible flows, and have thus been the dominant method used in the simulation of transonic and supersonic flows especially in aerodynamics applications. However, just as for pressurebased methods, a variety of techniques have over the years extended their ability to operate in low Mach and incompressible flow regimes. Turbomachinery applications is one area where competition between pressure-based and density-based solvers is still the norm in commercial, academic and open source codes, with both methods being used in diverse research groups and communities. While an extensive study would be required to clearly determine and evaluate the strength and weaknesses of these methods in this application area, the aim of this paper is to gain a better appreciation of the performance and accuracy of two state of the art codes, namely LINARS a density-based code developed at Graz University of Technology and coupledFoam, a pressure-based coupled solver developed on top of the OpenFOAM TM toolbox, noting that both solvers resolve the Navies Stokes equations in a coupled fashion.

INTRODUCTION

Pressure-based solvers were originally developed in the 70's [START_REF] Patankar | A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows[END_REF] for the solution of low-speed incompressible flows on structured staggered grids, they were later extended in the 80' and 90's to solve compressible flows in the subsonic, transonic and supersonic regimes on unstructured collocated grids [START_REF] Moukalled | A Unified Formulation of the Segregated Class of Algorithms for Fluid Flow at All Speeds[END_REF][START_REF] Demirdzic | Collocated Finite Volume Method for Predicting Flows at All Speeds[END_REF]. The modification was possible by changing the pressure equation from an elliptic form to a hyperbolic form with the addition of a pseudoadvection term that increases in strength with the Mach number [4, [START_REF] Burgree | Studies of Pressure-Velocity Coupling Schemes for Analysis of Incompressible and Compressible Flows[END_REF][START_REF] Issa | The Computation of Compressible and Incompressible Recirculating Flows by a Non-iterative Implicit Scheme[END_REF]. Density-based solvers on the other hands have their applications mainly in the aeronautics industry and compressible flows [START_REF] Sk | A difference scheme for numerical computation of discontinuous solution of hyperbolic equation[END_REF][START_REF] Lax | Systems of conservation laws[END_REF][START_REF] Hung | Numerical Solutions of Supersonic and Hypersonic Laminar Compression Corner Flows[END_REF][START_REF] Maccormack | A numerical method for solving the equation of compressible viscous flow[END_REF]. Through the use of a variety of pre-conditioning techniques density-based methods have also been extended to operate over a wide range of flow conditions including low Mach number and incompressible flows [START_REF] Choi | The application of preconditioning in viscous flows[END_REF]. The preconditioning results in the reformulation of the density equation into some form of pressure equation.

In both families of methods the velocity field is computed from the momentum equations. In densitybased solvers, the continuity equation is used to compute the density field while the pressure field is determined from the equation of state. In pressurebased solvers, the pressure field is computed by solving a pressure or pressure correction equation formulated from a combination of the continuity and momentum equations. The density field is then computed from the equation of state. Still an important distinction exists between the two families of methods in terms of the numerical approach used in each for the time linearization of the Navier-Stokes equations. In pressure-based methods, a SIMPLE [START_REF] Moukalled | A High Resolution Pressure-Based Algorithm for Multiphase Flow at all Speeds[END_REF] based algorithm is generally used to reformulate the continuity equation, while in density-based methods a Newton linearization is usually applied to the whole set of equations. Details on each of these methods can be found in the literature [START_REF] Hirsch | Numerical Computation of Internal and External Flows[END_REF][START_REF] Moukalled | The Finite Volume Method in Computational Fluid Dynamics: an Advanced Introduction with OpenFOAM TM and Matlab[END_REF]. The objective of this paper is to study the performance and accuracy of two state of the art codes [START_REF] Bader | Steady and Unsteady CFD Calculation of the Laminar ago Turbulent Transition in a Turning mid Turbine Frame with Embedded Design[END_REF][START_REF] Mangani | Development of a Pressure-Based Coupled CFD Solver for Turbulent and Compressible Flows in Turbo-Machinery Applications[END_REF] that use these two respective approaches, through the solution of a jet engine like turbine configuration, namely a high pressure transonic stator and a high pressure rotor. The two codes are first described, then the two test configurations are presented. This is followed by a comparison of the simulation results of the rotor test c a s e w i t h e x p e r i m e n t a l d a t a . F i n a l l y t h e convergence characteristics and computational times obtained from the two codes are discussed.

THE LINARS CODE

LINARS is the in-house CFD code developed at Graz University of Technology by Pecnik et al. [START_REF] Pecnik | Numerical Investigation of the Secondary Flow of a Transonic Turbine Stage Using various Turbulence Closures[END_REF]. Since then it has been the focus of continuous development that extended its applications with new models and increased its robustness and accuracy with new schemes and improved numerics. It has been successfully utilized for the solution of numerous applications [START_REF] Sanz | Numerical investigation of the effect of tip leakage flow on an aggressive S-shaped intermediate turbine duct[END_REF][START_REF] Bader | Flow evolution through a Turning Mid Turbine Frame with embedded design[END_REF][START_REF] Vader | Unsteady CFD simulation of a turning mid turbine frame with embedded design[END_REF][START_REF] Heschl | Evaluation and improvements of RANS turbulence models for linear diffuser flows[END_REF]. The code solves the compressible Reynolds-averaged Navier-Stokes equations in conservative form by means of a fully-implicit time-marching finite-volume method. Structured grids are utilized in multi-block assignment. The inviscid fluxes are discretized with the upwind flux-difference splitting method of Roe [START_REF] Roe | Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes[END_REF]. A higher order of spatial accuracy for the convective fluxes is achieved through monotone upstream-centered schemes (MUSCL). Generally, a third-order spatial discretization is applied. In order to avoid numerical instabilities the total variation diminishing scheme (TVD) is applied. The TVD scheme switches to first order accuracy in regions of high state vector gradients. The viscid flux vector at the cell interfaces is constructed in a centraldifferencing manner after transformation using Green's theorem. A linear set of algebraic equations is obtained by discretization in time with the Newton-Raphson procedure. The linearization of the inviscid fluxes is spatially of first order. The viscid fluxes are linearized with the thin-layer approximation to obtain a block tridiagonal matrix of the implicit side for each grid index line. The linear equation set is solved by the alternating direction implicit scheme. Convergence of steady state simulations is improved by using a local time step based on a local stability criterion and a multi-level multi-grid V-cycle. The main flow equations, the turbulence equations, and the transition equations are solved sequentially. For turbulence modeling the one-equation turbulence model by Spalart and Allmaras [START_REF] Spalart | A One-Equation Turbulence Model for Aerodynamic Flows[END_REF] (SA) and the two-equation shear stress transport (SST) model by Menter [START_REF] Menter | Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications[END_REF] were implemented. The reader is referred to the cited references for details about the models. In order to consider boundarylayer transition the γ-Reθ correlation-based transition model by Menter et al. [START_REF] Menter | A correlation based transition model using local variables part 1 -model formulation[END_REF] with the modification introduced by Langtry and Menter [START_REF] Langtry | Transition Modeling for General CFD Applications in Aeronautics[END_REF] was implemented.

The coupledFoam CODE

coupledFoam is a fully coupled pressure-based solver implemented within the OpenFOAM TM framework based on the fully coupled algorithms of Darwish et al. [START_REF] Darwish | A Fully Coupled Navier-Stokes Solver for Fluid Flow at All Speeds[END_REF] that accounts for the pressure velocity coupling more comprehensively. Over the past few years new development in the solver has greatly improved its robustness and performance [START_REF] Mangani | Development of a Pressure-based coupled CFD solver for Turbulent and Compressible Flows[END_REF]. An implicit diffusion discretization [START_REF] Lipnikov | Minimal stencil finite volume scheme with the discrete maximum principle[END_REF] is now used for the pressure equation, while the Algebraic Multigrid linear solver (AMG) now boasts new features that greatly enhance its performance when dealing with ill-conditioned matrices that frequently arise in compressible flows. Finally the numerics of the turbulence equations has also experienced numerous improvements to ensure that the models cope with the rapidly converging velocity and pressure fields. The reader is referred to [START_REF] Darwish | A Fully Coupled Navier-Stokes Solver for Fluid Flow at All Speeds[END_REF] for more details on the numerical discretization and velocity-pressure algorithm used in the coupled solver. Thus the discretized equations in any control volume resemble the pattern shown in Figure 1.

$ Figure 1. Coupled system of discretized equations at each finite volume

The discretized equations representing the Navier-Stokes equations, in the case of LINARS are solved as one system of equations including now the energy equation.

TEST CASE DESCRIPTION

The selected test case is based on the two-stage transonic test turbine that is operated by the Institute for Thermal Turbomachinery and Machine Dynamics at Graz University of Technology for flow and acoustic investigations. It is a continuously operating two-stage cold-flow open-circuit plant. In Figure 2 the meridional flow path through the twostage test turbine is plotted. The turbine consists of 24 high-pressure vanes, 36 un-shrouded HP rotor blades, 16 strut blades within an S-shaped turning mid-turbine frame (TMTF) and 72 shrouded low pressure rotor blades rotating in counter-clockwise direction. This design has been developed within the framework of the EU Project DREAM. As shown in Figure 3 the air flowing into the HP turbine is accelerated in circumferential direction by the vanes before entering the rotor. It leaves the rotor with a negative swirl which differs remarkably between hub and shroud section. Afterwards it is turned by the struts of the TMTF opposite to the direction of rotation of the HP rotor. The air then enters the LP rotor which rotates in the opposite direction of the HP rotor at about one third of its speed Measurements were performed in axi-normal planes in front of and behind the TMTF and behind the LP rotor. For this numerical study only the HP stage is used. The flow through the stator and then through the rotor are calculated separately. The outlet plane of the rotor simulation corresponds to the measurement plane C, so that a comparison with measurement data can be done there.

• ! ! ! ! • ! ! ! ! • ! ! ! ! • ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ C • • • • ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ C + • ! • ! • ! ! ! ! • ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ NB • • • • ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ NB ∑ NB = • • • • ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ C

COMPUTATIONAL DETAILS

The two-equation shear stress transport (SST) turbulence model [START_REF] Menter | A correlation based transition model using local variables part 1 -model formulation[END_REF] was used in both codes and an automatic wall treatment was employed for wall resolution [START_REF] Menter | Zonal Two Equation Turbulence Model For Aerodynamic Flows[END_REF] in coupledFoam.

For the convergence residuals and total integral quantities at the outlet were monitored. In case of the pressure-based solver the calculations are stopped when the residual drop below 1.e-5, while the convergence is usually reached already for 1.e-4.

Computational meshes

Several body fitted hexahedral meshes were generated for both stator and rotor simulations with an increasing size, as shown in Table 1. For the stator in addition to the structured girds (Hexa1 and Hexa2) an unstructured grid was generated so as to evaluate the ability of the pressure-based solver to handle polyhedral meshes, the mesh is shown in Figure 4. The three meshes of the rotor with increasing cell numbers consist of 8 blocks. Special emphasis has been laid on the generation of a smooth mesh in the tip gap, as shown in Figure 5, by adding here additional blocks. Clustering and refinement of the mesh close to the wall were adopted in order to achieve an average y+ of 1.

$ $

. Rotor mesh detail: the tip gap is fully discretised.

Boundary conditions

At the inlet of the stator constant values for total pressure, total temperature and flow angle as well as for the turbulent quantities are imposed. At the outlet the static pressure at a given radius is set assuming radial equilibrium. The non-reflecting boundary treatment according to Giles has been applied. At the inlet of the rotor a radial distribution of the boundary values has been imposed taken from a former full stage simulation where the flow quantities were extracted at the interface. Again a radial equilibrium static pressure profile was imposed at the outflow. Periodicity boundary conditions were adopted in order to reduce memory and computational time and to capture the influence of the flow in the pitchwise direction. A no slip and adiabatic conditions were applied to the walls.

RESULTS AND DISCUSSION

Stator blade

For the stator blade simulation, LINARS and coupledFoam were used with meshes Hexa1, Hexa2 and only coupledFoam for mesh Tetra1. For the stator blade simulation no experimental measurements are available and than comparisons are limited to the CFD results between both codes.

The coupledFoam code use a false transient formulation with a physical timestep that corresponds to a mean Courant number (CFL) of 300 and a maximum of 10000. LINARS instead use a local CFL of 10. An interesting aspect that was investigated is the scalability with mesh size of coupledFoam, that is the convergence characteristics of the solver with increasing mesh size. As demonstrated in [START_REF] Mangani | Development of a Pressure-Based Coupled CFD Solver for Turbulent and Compressible Flows in Turbo-Machinery Applications[END_REF], coupledFoam is mesh scalable when applied to steady state incompressible flow simulations, that is it requires a nearly constant number of iterations to converge independently of mesh size. For compressible and turbulent flows the additional couplings resulting from the energy equation are not implicitly accounted for, resulting in a slight deterioration of the scaling behaviour. The scalability can be assessed in Figure 6 Table 2 shows some difference in the results obtained from LINARS and coupledFoam for Hexa2 Mesh. The results pertain to pressure losses and Mass flux error with LINARS yielding a higher pressure loss and higher Mass Flow error.

Table 2. Total pressure losses and Mass flow percentage error

However as shown in Figure 7 and Figure 8 which depicts contour plots of static pressure at the blade, overall results from LINARS and CoupledFoam are comparable. At the pressure side (Figure 7) both codes predict a strong deceleration at the leading edge region before the pressure remains nearly constant. On the suction side (Figure 8) a strong acceleration occurs up to about 70 % chord length before a strong pressure increase (dark blue zone at the hub) is caused by a shock. Both codes predicts similar expansion of the fluid with slightly differences in the shock region. The shock is predicted in the same axial position with a bigger pick in coupledFoam but with a general smoother behaviour. The tendency to a smooth solution is also evident in the total pressure contour maps at the outlet as shown in Figure 9. The boundary layers at the shroud are similar, but at the hub LINARS predicts a more pronounced zone of low pressure. The overall accuracy and agreement of both codes are quite good bearing in mind the different algorithms used for the pressure-velocity coupling, and can be due to the difference in the used discretization advection schemes.

Rotor blade

The HP rotor was simulated as a standalone blade with appropriate radial profiles at the inlet based on a previous full stage simulation with a mixing plane interface performed in LINARS. Similar to the stator blade, the coupledFoam code use a false transient formulation with a physical timestep that corresponds to a mean Courant number (CFL) of 300 and a maximum of 10000. LINARS instead use a local CFL of 10. For this case experimental data were available in terms of circumferentially averaged profiles downstream the rotor blade corresponding to the section C in Figure 2. Pitch and yaw angles, as well as axial and circumferential absolute velocity profiles were plotted against experimental results.

Scalability Analysis

In the rotor simulation three hexahedral meshes, denoted by Hexa1, Hexa2 and Hexa3 were used for the linear convergence analysis of coupledFoam.

Figure 10 shows that even for a moving reference frame the linear scalability of the coupledFoam solver is retained. For these runs the convergence of the mass average total temperature at the outlet was monitored. This approach is sometimes used to ensure that the simulation is fully converged. In Figure 10, the convergence characteristics for the HEX1, HEXA2 and HEXA3 meshes are shown, for all three meshes the total temperature solution converged within 50 iterations, i.e equivalent for a residual valour of 1.0e-4, this was similarly observed in other simulations [START_REF] Mangani | Development of a Pressure-Based Coupled CFD Solver for Turbulent and Compressible Flows in Turbo-Machinery Applications[END_REF]. Furthermore, the convergence characteristics of the three meshes are nearly identical, which indicates that the solver is all scaling linearly with the mesh size.

Accuracy Analysis

Table 3 shows the Rotor performance as computed with LINARS and coupledFoam for Hexa2 Mesh.

Results for Hexa3 and Hexa1 were similar. Results of both solvers are very similar with the coupledFoam yielding a slightly higher value for Rotor performance and a lower Mass flow Error. Calculated and measured circumferential averaged profiles for both LINARS and coupledFoam, are shown in Figure 11. The general agreement is quite good for all the quantities.It is interesting that coupledFoam predicts most secondary effects to be closer to the shroud. This is especially evident for the tip leakage flow where coupledFoam gives a higher axial velocity peak closer to the shroud. The higher peak agrees better with the measurements whereas its location is better captured by LINARS. The discrepancies between computed and experimental results can be partly explained by the steady simulation of the very unsteady flow and by the missing interaction with the following TMTF and LP stage.

$

A full unsteady simulation of the entire test rig should be the focus of future work.

CONCLUSIONS

Simulations on the stator and the rotor of the high pressure stage were performed using two codes with different numerics, one using a pressure-based method, coupledFoam and the other using a density-based method, LINARS. Results from both codes were shown to be very similar and more importantly it was shown that computed results were comparable to experimental data. Difference between the computed results of the two codes could be easily attributed to difference in the advection schemes used rather that to the adopted algorithmic method, especially for shocks resolving. Evidence can be found for the outlet total pressure counters shown in figures 7, 8 and 9 for the stator case. This issue will be investigated in future work through the use of similar schemes for the discretization of diffusion and advection terms.

Figure 2 .

 2 Figure 2. Meridional section of the test setup showing the HP stage between planes A and C, and the LP stage between C and F.

Figure 3 .

 3 Figure 3. Streamwise section showing the blade profiles at mid section with their numbers and the sense of rotation.

Table 1 .

 1 Mesh size and type: Hexa (hexahedral elements), Tetra (tetrahedra and prismatic elements).

Figure 4 .

 4 Figure 4. Stator mesh detail: tetrahedral and prismatic

Figure 6 .

 6 Figure 6. Residuals and mass imbalance convergence for the pressure-based solver.

Figure 7 .

 7 Figure 7. Pressure side static pressure contour map: (a) coupledFoam upper, (b) LINARS.

Figure 8 .

 8 Figure 8. Suction side static pressure contour map a) coupledFoam, b) LINARS

Figure 9 .

 9 Figure 9. Outlet total pressure contour map: (a) coupledFoam, (b) LINARS.

$!Figure 10 .

 10 Figure 10. Residuals, total temperature and mass imbalance convergence for the pressure-based solver

Figure 11 .

 11 Figure 11. Circumferential averaged flow profiles at the outflow plane

  A s c a l a b i l i t y s t u d y w a s a l s o c o n d u c t e d o n coupledFoam, results indicate that for this class of problems the coupled pressure-based solver retains very good scalability with mesh size, as demonstrated by the near constant number of iterations to convergence attained on multiple mesh sizes. A similar study will be performed on the density-based solver in future work.

Table 3 .

 3 Rotor Performance and Mass flow percentage error.

ACKNOWLEDGMENTS

The authors wish to acknowledge the support received from their respective Universities, HSLU Luzern, TUGraz and AUB.


Joury Temis

Mikhail Temis

Andrey Egorov

Valentin Gavrilov

Investigation of dynamic behavior of auxiliary power unit with rotor in gas foil bearings

Keywords:

Auxiliary power unit rotor static and dynamic characteristics were investigated for four rotor supporting schemes. Auxiliary power unit rotor supported in roller element bearings was compared to similar rotor supported in gas foil bearings and to intermediate option of rotor supported in combination of gas foil bearing and ball bearing. Support reactions under the action of weight, imbalance and flight acceleration forces are determined for all schemes. Rotor support reactions gives an opportunity to select gas foil bearing type and dimensions.

Rotor model for nonlinear analysis is based on beam finite elements and verificated with corresponding solid model by comparison of eigenfrequencies. This model taking into account supports casing stiffness characteristics determined using 3D finite-element models and nonlinear stiffness properties of roller element and/or gas foil bearings. Different schemes of rotor supporting are analyzed for support loads, eigenfrequencies and nonlinear vibration orbits and amplitudes that allows selecting major problems for upgrading of auxiliary power unit rotor with gas foil bearings.

INTRODUCTION

From one side application of gas foil bearings in supports of small gas turbine engines rotor allows in perspective to create a "dry" engine and changes limits of rotor rotational frequency. That sufficiently influences on engine structure, mass characteristics, reliability, cost of manufacturing and operation [START_REF] Heshmat | Advancement in the Performance of Aerodynamic Foil Journal Bearings-High Speed and Load Capacity[END_REF]. However, from another side application of gas foil bearings in rotor supports requires solution of a number of problems such as creating of sufficient carrying force, response on non-stationary loads, reliability at high temperatures etc. Most of these problems solved using different foils structure. Regardless all peculiarity of gas foil bearings at present time they find increasingly greater application in supports of small gas turbine engines [START_REF] Dellacorte | Remaining Technical Challenges and Future Plans for Oil-free Turbomachinery[END_REF].

There are large amount of works devoted to rotor in gas foil bearings operational characteristics investigation. The major part of them using experimental methods for rotor in gas foil bearings dynamics investigation as it presented in [START_REF] Rubio | Bump-type foil bearing structural Article Title -9 stiffness: experiments and predictions[END_REF][START_REF] Kim | Rotordynamic performance of an oil-free turbocharger supported on gas foil bearings: effects of an assembly radial clearance[END_REF]. However there are a number of works where numerical and experimental approaches are using together [START_REF] Walton | On the coupling of foil bearing supported rotors: part 1 -analysis[END_REF][START_REF] Tomaszewski | On the coupling of foil bearing supported rotors: part 2experiment[END_REF]. Apart of them paper regarding to numerical [START_REF] Le Lez | A new bump-type foil bearing structure analytical model[END_REF] and experimental [START_REF] Andres | Rotordynamic performance of a rotor supported on bump type foil gas bearings; experiments and predictions[END_REF][START_REF] Salehi | Advancements in the structural stiffness and damping of a large compliant foil journal bearing: an experimental study[END_REF] investigation of individual gas foil bearings that allows to investigate bearing characteristics for different elastic foils structure simulating various operational conditions.

Traditional schemes of high-speed auxiliary power unit rotor are well known. However, operation of specific engine is different from other due to a big number of stiffness and damping rotor-bearing-casing system parameters. Therefore, the aim of replacing of rolling element bearings with gas foil bearings for rotor of existing auxiliary power unit requires at first stage an investigation of engine parameters and it sensitivity to their changing.

Basing on mathematical models developed by authors [START_REF] Temis | Gasdynamic foil bearing model[END_REF][START_REF] Temis | Dynamics of compact gas turbine rotor supported by gas bearing[END_REF][START_REF] Temis | Numerical and Experimental Investigation of Rotor-simulator in Foil Gasdynamic Bearings for Compact Gas Turbine[END_REF] an investigation of dynamic behavior of auxiliary power unit supported in gas foil bearings or roller element bearings is carried out in present paper.

ENGINE CHARACTERISTICS

Auxiliary power unit used for investigation in current paper have a rotor scheme as presented in fig. 1 (Scheme 1). Rotor weight is about 3.5 kg and nominal rotating frequency 38 500 rpm. Engine have a one rotor with mounted one stage centrifugal compressor and one stage axial turbine. In initial configuration rotor is supported in one ball bearing in front support and one roller bearing in back support. So front support carry both part of radial load and full axial load.

All supports should use gas bearings in final upgraded rotor configuration. Proposed support designs should not change engine structure sufficiently. However, ordinary gas journal bearings have greater length then roller element bearings in existing engine. Besides this after changing of ball bearing with radial gas bearing, the thrust gas bearing should be installed for compensation of axial force. Thrust bearing also needs a sufficient radial space for a runner. Engine structure allows several schemes for using gas bearings in rotor supports. Usually radial and thrust gas bearings located between compressor and turbine. However, due to limited distance between compressor and turbine in existing engine there is small base length between centers of radial supports in such scheme (fig. 1, Scheme 4). So for increasing lateral stability of the rotor the supplementary part was installed at the back where radial and thrust gas bearings was mounted (fig. 1, Scheme 3). Also intermediate rotor scheme with one ball bearing in front support and one radial gas bearing mounted on supplementary rotor part as rotor back support (Scheme 2) is presented in fig. 1b. This scheme allows only to change bearing type in hot part of engine.

Figure 1. Power unit rotor schemes

Comparison of presented supporting schemes eigenfrequencies, radial loads distribution and orbits during startup and operation conditions allows to show advantages of each scheme.

ROTOR MODELS

Rotor finite element solid models corresponding to each rotor supporting scheme as presented in fig. 1 are developed for investigation (fig. 2). Rotor was simulated by 20-node finite elements, compressor and turbine blades simulated as disks with corresponding density and stiffness. For all tighten rotor elements contact on faces was simulated as bonded.

These models are used for calculation of supports reactions and stress-strain state under the action of gravity and operational loads. Results for support reactions in all schemes presented in table 1 for four load cases. In load case I rotor is fixed and only weight force (g) is acting. In load case II rotor rotating at maximum operating frequency and weight force and imbalance inertia force (me) are acting. For load cases III and IV, besides rotor imbalance inertia force the acceleration during airplane horizontal (2g) and vertical (4g) evolution is taken into account. Reactions values in table 1 give information of maximum support loads at startup and operation for further selection of gas foil bearing dimensions and structure. Gas bearings should provide rotor floating-up at startup and compensation of operational loads.

According to presented results radial gas foil bearing should be designed for radial load at startup for load about 30 N and at evolutions in operational conditions for load up to 150 N. In rotor dynamic analysis, the beam rotor models are used. For improvement of beam models in simulation of stiffness characteristics for complex geometry rotor details the special finite elements with general 6x6 matrix are used. Such general matrix is calculated using detail 3D models of rotor elements. There are gratifying correspondence between results for all models after verification of beam model versus 3D model, (table 2).

3D model

Bernoulli beam model

GAS BEARINGS SELECTION

The gas foil bearings with one top foil and bump foil are selected for current investigation (fig. 4а). Mathematical models for presented bearing for different shaft journal diameters and bearing length are created. Gas foil bearings carrying force and attitude angle calculated on the base of bearing mathematical model developed in [START_REF] Temis | Gasdynamic foil bearing model[END_REF]. This model is used nonlinear Reynolds equation for compressible fluid for calculation of gas flow in bearing. The step process for shaft eccentricity in bearing with self-correcting procedure [START_REF] Temis | Selfcorrection Step by Step Method for Solution of Nonlinear Elasticity and Plasticity Problems[END_REF] at each step is used for solution of nonlinear Reynolds equation. For determination of top foil radial deflections the 2D contact interaction model between top foil, bump foil and bearing race are created (fig. 4a). This model includes elastic Coulomb friction model and provides an actual bump foil circumferential displacement. Contact interaction model taking into account friction interaction between bearing top foil and bump foil, bump foil and bearing race with friction coefficient depending on foils and bearing race material and coating. Friction coefficient varying in range between 0.1 and 0.3 in current models. Discrete contact interaction of top and bump foils allows to simulate top foil deformations between bumps. Carrying out calculations for shaft journal diameters and bearing length in range of values that conforms to major engine dimensions allows to determine bearing diameter and length array satisfying by carrying force for support reaction values in table 1.

Bearing diameter of 30 mm equal to rotor diameter in support area is chosen from this array. Radial gas foil bearing parameters is presented in table 3. Bearing carrying force and attitude angle presented in fig. 5 and6 for rotor rotating frequency of 5000 rpm and support temperature of 20°C and 400°C correspondingly. Bearing characteristics are represented in terms of the dimensionless eccentricity ratio χ = e/δ, where e is a shaft journal eccentricity and δ is a radial clearance in bearing. According to operating parameters of engine, there is an axial force need to be compensated by thrust foil bearing. Thrust bearing characteristics selected on the analogy of the data presented in [START_REF] Gad | Performance characteristics of gas-lubricated bump-type foil thrust bearing[END_REF]. Using in investigation gas foil bearings 3D solid models presented in fig. 4b and4c for different rotor supporting schemes. For Scheme 1 and Scheme 2 the rolling element bearings stiffness need to be determined for support finite element considering bearings nonlinear characteristics. This was done using Hertz contact theory [START_REF]Rolling element bearings. Calculation, design and service of supports[END_REF]. Calculated bearing stiffness are К1 = 2•10 8 N/m (B1) and К2 = 3•10 8 N/m (B2).

Gas foil bearing linearized stiffness values corresponded to shaft equilibrium position in bearing in operation regime are presented for a number of rotating frequencies in table 4.

Angular stiffness for thrust bearing is КRot_u = 4.9•10 3 N•m/rad (Schemes 3-4).

ROTOR EIGENFREQUENCIES ESTIMATION

Rotor supports stiffness sufficiently changes from Scheme 1 to others due to replacing of rolling element bearings with gas bearings and changing of support location.

For engine in gas bearings operating capacity it eigenfrequencies, eigenmodes and critical speeds for each supporting scheme should be determined and correlated with range of rotor rotating frequencies. Engine maximum operating speed is 42000 rpm. Rotor finite element solid models (fig. 2) that taking into account rotor gyroscopic moments are used for calculation. Eigenmodes, eigenfrequencies and Campbell diagrams for four rotor supporting schemes are presented in fig. 7.

Replacing of roller element bearings with gas foil bearings brings to sufficiently decreasing of supports stiffness. Besides this in Scheme 5 for all schemes. Rotor for all four schemes have one similar eigenmode: angular vibrations of rotor as rigid body due to casing angular small stiffness. This mode corresponds to first critical speed f1 for Scheme 1 and Scheme 4. It is decreased for Scheme 4 in comparison with Scheme 1 on 15% by decreasing of radial support stiffness. Angular vibrations of rotor as rigid body also corresponds to first critical speed f1 for Scheme 2 and for second critical speed f2 for Scheme 3 and it is increased on 64% for Scheme 2 and on 72% for Scheme 3 in comparison with Scheme 1 first critical speed value (f1). Increasing of corresponding critical speed for Scheme 2 explained by increasing distance between supports B1, B2 and individual support for B2. Besides this in Scheme 3, the thrust bearing was installed and this explain critical speed growth in comparison with Scheme 2.

Another mode for Scheme 1 and Scheme 2 is a lateral rotor bending vibrations in supports. Corresponding critical speed for Scheme 1 (f2) and Scheme 2 (f2) have close values. Influence of rotor supports location and B2 support stiffness change appears by slight decreasing of critical speed for Scheme 2.

Another mode for Scheme 3 (f1) and Scheme 4 (f1) is a lateral rotor vibration as rigid body in gas foil supports. It have less value of critical speed for Scheme 4 because of location of B1 and B2 supports on same console (fig. 1).

All eigenfrequencies values are increasing with rotating frequency growing due to gyroscopic moments (all schemes) and increasing of gasdynamic stiffness (schemes 2-4). The gyroscopic moment influence on eigenmode value is sufficient for eigenmodes where rotor angular displacement is dominant (Scheme 3 -f2, Scheme 4 -f1).

For all schemes rotor passing through first critical speed at running up in range of rotating frequencies 7500-11500 rpm. For Scheme 1 second rotor critical speed is equal to 40500 rpm and greater then rotor maximum operational speed. For Scheme 2 the second rotor critical speed (39000 rpm) dropped almost until maximum operation speed. First and second critical speeds for schemes 3 and 4 are close to each other and lie in range of frequencies 7500-11500 rpm. There is a big region for Scheme 2 and Scheme 3 where eigenfrequencies are close to rotor frequency.

ROTOR DYNAMIC BEHAVIOR INVESTIGATION

On fourth stage, the rotor dynamic behavior in whole range of rotating frequencies was investigated and rotor orbits in bearing were determined (fig. 891011). Gas foil bearings under the action of dynamic radial loads caused by rotor imbalance and non-stationary loads was investigated. In each support the imbalance force of 1 g•mm is applied and normal gravity force acting on all rotor model. For direct integration of rotor nonlinear equations the Newmark scheme (δ = 1/2 and α = 1/4) with iterative refinement regarding to bearing carrying force is implemented.

As demonstrated in fig. 9 and 11 the simulation of rotor in gas foil bearings dynamics allows occurrence of subharmonic vibrations for small structural damping in system. These vibrations started when rotor speed approaches to first critical speed and lasting in some range. This range is shorter for hot supports conditions. Rotor orbits in both supports have elliptical or even more extended shape in this range. Rotor vibrations corresponds to first mode and have a big magnitude. When increasing rotor rotation frequency the rotor rotates on stable regimes around equilibrium position with small amplitude.

Stable regimes of rotor rotation are received in rotor dynamics simulation for structural damping of 0.003. All rotor orbits for both cold and hot conditions are circular and amplitudes are small (fig. 8 and10).

CONCLUSION

An opportunity of auxiliary power unit design changing for implementation of gas foil bearing in rotor supports is shown. Bearing parameters including dimensions, geometry etc. for providing required carrying force are determined. Several schemes of rotor supports replacing with gas foil bearings are proposed. Analysis of support loads in operational and overload regimes as well as eigenvalue analysis and dynamic analysis shows working capacity of rotor supported in gas foil bearings. All presented schemes involves small modification of exist engine structure and this limiting the changes need to be performed for replacing of roller type bearings with gas foil bearings.

Figure 2 .

 2 FE model of rotor

  3). Casing stiffness С1 (in plane section of support B1): Кu = 7.5•10 7 N/m, КRot_u = 2.07•10 4 N•m/rad. Casing stiffness С2 (cylindrical casing between supports B1 and B2): Кu = 5.2•10 7 N/m, КRot_u = 3.6•10 5 N•m/rad. Stiffness of casing C3 is Кu = 5•10 9 N/m.

Figure 3 .

 3 Figure 3. Casing FE model and deformed geometry

  2 and Scheme 3 distance between supports B1 and B2 is increased. Casing of support B2 have greater stiffness regards to individual connection to engine casing in Scheme 2 and Scheme 3 instead of console connection (fig. 1) for Scheme 1 and Scheme 4. a) radial foil bearing scheme and finite-element model b) radial bearing solid model c) thrust bearing solid model

Figure 4 .

 4 Figure 4. Gas foil bearings Critical speeds for forward precession represented in table 5 for all schemes. Rotor for all four schemes have one similar eigenmode: angular vibrations of rotor as rigid body due to casing angular small stiffness. This mode corresponds to first critical speed f1 for Scheme 1 and Scheme 4. It is decreased for Scheme 4 in comparison with

Figure 5 . 6 .Figure 7 .Figure 8 .Figure 9 .Figure 10 .Figure 11 .

 567891011 Figure 5. Gas bearing characteristics (T = 20°C)

Table 1 .

 1 Reactions in rotor supports Scheme 1

			Scheme	Scheme	Scheme
			2	3	4
	Rotor mass, kg	3,63	3,99	4,28	3,93
		Reaction forces in B1, N
	I (g	13,87	24,71	23,56	22,72
	II (g+me)	22,87	33,71	32,55	32,9
	III(2g+me)	35,96	59,82	57,27	56,1
	IV(4g+me)	78,37	132,55	126,78	123,76
		Reaction forces in B2, N
	I (g	22,42	15,21	19,27	16,59
	II (g+me)	31,42	24,21	28,28	24,4
	III(2g+me)	54,75	38,88	47,8	41,19
	IV(4g+me)	121,1	85	105,4	90,77
	Support finite element used in rotor model taking into
	account bearing stiffness and support casing stiffness.
	Bearing stiffness determined by special models depending
	upon bearing type and structure. Casing stiffness in bearing
	position determined by finite element model (fig.

Table 2 .

 2 Rotor beam model verification

		№	Eigenvalue, rpm Solid model Beam model	, %
	Scheme	1	6055	6109	0,89
	1	2	35905	32675	-9
	Scheme	1	7535	7571	0,48
	2	2	35338	32185	-8,9
	Scheme	1	7974	7609	-4,6
	3	2	8073	8078	0,1
	Scheme	1	4943	4671	-5,5
	4	2	7093	7241	2,1

Table 3 .

 3 Foil bearing parameters

	Bearing diameter D1, mm	30
	Length, mm	42
	Number of top foils	1
	Bump foil thickness, mm	0.1
	Top foil thickness, mm	0.1

Table 4 .

 4 Rolling and gas foil bearing (Т = 20°С) linearized stiffness

		Rotating	Stiffness, N/m
	№	frequency, rpm	B1	B2
	Scheme1	all	2•10 8	3•10 8
		5000		1.02•10 6
	Scheme 2	20000	2•10 8	5•10 6
		42000		8.65•10 6
		5000	1.74•10 6	1.31•10 6
	Scheme 3	20000	5.36•10 6	5.19•10 6
		42000	9.31•10 6	8.98•10 6
		5000	1.64•10 6	1.135•10 6
	Scheme 4	20000	5.33•10 6	5.07•10 6
		42000	9.25•10 6	8.76•10 6

Table 5 .

 5 Critical speed

		Critical speed (forward precession),
	№	rpm
		f1	f 2
	Scheme1	6700	40500
	Scheme 2	11000	39000
	Scheme 3	9000	11500
	Scheme 4	5700	7500


Mikhail Temis
email: mikhail.temis@gmail.com

Alexander Lazarev

Influence of Centrifugal Forces on Oil Flow in Journal Bearing of Planetary Gear

Keywords:

Mathematical model of oil flow in fluid film bearing in field of centrifugal forces is developed. Centrifugal forces for planet wheel bearing sliding surfaces and oil gap are formulated. This model is based on modification of two-dimensional Reynolds equation taking into account inertia centrifugal forces for oil film. Required modification of Reynolds equation is received from Navier-Stokes and continuity equations taking into account centrifugal forces acting on planet wheel bearing. Modified 2D Reynolds equation is solved numerically using finite-element discretization. Developed mathematical model is verificated at comparison with solution of full Navier-Stokes equations system obtained in commercial software package. Results for pressure distribution for bearing with fixed axis and for planet wheel bearing are received and compared. The sufficient influence of centrifugal inertia forces in oil layer of planet wheel bearing on pressure distribution, bearing carrying force and attitude angle is shown for specific shaft journal eccentricity ratio, eccentricity direction and rotation velocity.

INTRODUCTION

Planetary gears have a wide application in different areas of industry. At present moment, they find application in perspective geared turbofan aircraft engine [START_REF] Kurzke | Fundamental Differences Between Conventional and Geared Turbofans[END_REF]. Integration of planetary gear in gas turbine engine as a mechanism for transmitting of rotation from low-pressure rotor to fan rotor gives an opportunity for choosing of optimal aerodynamic and structural parameters of both rotors [START_REF] Riegler | The Geared Turbofan Technology Opportunities, Challenges, and Readiness Status[END_REF]. In present moment a single-row planetary gear (Figure 1a) is used for current purposes. Fluid film bearings used in supports for high speed or heavy-loaded gears. Main characteristics of fluid film bearing such as stiffness and damping based upon hydrodynamic fluid pressure caused by relative motion of sliding surfaces. In most of applications, fluid inertia forces are negligible in comparison with hydrodynamic forces, but if some applications their influence on bearing characteristics could be sufficient and should be taken into account. Planet wheel journal bearing are an example where influence of fluid inertia forces have an influence on bearing characteristics.

Parameters of fluid flow in bearing with fixed axis usually calculated by Reynolds equation [START_REF] Braun | Cavitation Formation and Modeling for Fluid Film Bearings: A Review[END_REF]. However, conventional Reynolds equation form received from Navier-Stokes and continuity equations while neglecting inertia forces. Sufficient linear velocity of planet wheel bearing rotating around carrier velocity leads to increasing of contribution of centrifugal inertia forces in pressure distribution in bearing, bearing carrying force value and direction. For taking into account inertia forces acting on oil film in journal bearing of planet wheel the conventional mathematical model for oil flow in journal bearing based on Reynolds equation requires modification.

INERTIA FORCES

For any type of planetary gear each planet wheel [START_REF] Riegler | The Geared Turbofan Technology Opportunities, Challenges, and Readiness Status[END_REF] participating in compound motion: rotation with carrier (H) with angular speed H and rotation about self-axis with angular speed 2 (Figure 1a). Relation between carrier and planet wheel angular speeds for single-row planetary gear is as follows

3 2 2 1 H z z    , ( 1
)
where z2 and z3 are number of teeth of planet wheel and epicycle correspondingly. One sliding surface of bearing is a part of carrier and another is a part of planet wheel. The relative motion of sliding surfaces with angular speed 2 causes fluid velocity distribution and therefore hydrodynamic pressure in bearing gap. Planet wheel participating in compound motion: rotation with carrier (H) with angular speed H and rotation around planet wheel bearing axis with angular speed 2. Thus both sliding surfaces "H" and "2" (Figure 1b) of planet wheel journal bearing rotating with angular speed H about axis OH. And sliding surface "2" also rotating about axis O2. Accelerations in fluid film are defined by sliding surfaces motion. Accelerations for sliding surfaces in bearing are shown in Figure 1b. Acceleration in fluid film are consist of vector sum of transfer (ae), relative (alub) and Coriolis (ac) acceleration components which are determined as follows in cylindrical coordinate system O2rφz. [START_REF] Temis | Stiffness and Damping Characteristics of Journal Bearing with Flexible Working Surfaces[END_REF] applying assumptions for fluid flow in thin film. These assumptions allow introducing dimensionless variables, coordinates and constants in following form [START_REF] Temis | Contribution of Bearing Structure in Gas Turbine Power Unit Rotor Dynamics[END_REF] s sR

MATHEMATICAL MODEL

Required modification of Reynolds equation taking into account mean values of fluid inertia force (3) one can receive from Navier-Stokes and continuity equations

 , yy h   , zz R  , uu V  , (/ ) vv hR V  , ww V  , ( 4
) m h h h  , 0 p p p  , Vt t R  , m h R  , Re Vh    ,
where V = 2R is a specific linear velocity on sliding surfaces, hm is an average fluid film thickness, ρ and η are fluid film density and dynamic viscosity correspondingly. Taking into account nondimensionalization (4) Navier-Stokes equations for laminar isothermal flow of incompressible fluid in bearing can be written in coordinate system sy'z (Figure 2

                                                            2 div , 3 lub v z                , ( 5
)
where dimensionless fluid inertia forces

2 2 22 sin 2 HH H s r f h R       , 2 2 2 22 1c o s2 HH H y r f uu R          (6)
All dimensionless variables and their derivatives have same order of magnitude. Thus order of magnitude of terms in ( 5) and ( 6) are specified by coefficient ~10 -3 and Reynolds number Re. While neglecting of terms with less order of magnitude in ( 5) and ( 6) the Navier-Stokes equations will have form

                               , ( 7
)
and modification of Reynolds equation with taking into account centrifugal inertia forces for planet wheel bearing will receive from (7) as follows

33 2 3 2 6s i n HH p ph s hh R r h sszz s s R                         . ( 8
)
Numerical solution of Reynolds equation (8) carried out using finite-element discretization procedure. Special triangular finite element for fluid film pressure is used. Developed bearing model taking into account carrier and planet wheel rotations and allows calculating pressure distribution in bearing for various relations between H and 2 for any shaft journal eccentricity caused by gears of planet wheel with sun wheel and epicycle.

MODEL VERIFICATION AND RESULTS

Bearing mathematical model was verified for the case of long bearing by comparison with analytical solution and numerical solution in STAR-CD software based on full Navier-Stokes equations. Calculations was performed for parameters: bearing radius R = 15 mm, distance between planet wheel and carrier centers rH = 167 mm, radial gap in bearing δ = 0,05 mm, oil viscosity η = 0,02 Pa•s and density ρ = 900 kg/m 3 , planet wheel rotation frequency n2 = 15000 rpm, carrier rotation frequency nH = 6000 rpm, ambient pressure p0 = 0,1 MPa. A model of long bearing was created in STAR-CD for verification (Figure 3). Simulation of long bearing was performed by special boundary conditions on bearing calculation model faces: Velocity and acceleration components in direction Oz is equal to zero. STAR-CD model is used a full Navier-Stokes equation for laminar flow at constant temperature distribution without slipping motion of fluid. Finite volumes method is used for calculation. Bearing model in STAR-CD take into account all components of fluid inertia force [START_REF] Braun | Cavitation Formation and Modeling for Fluid Film Bearings: A Review[END_REF]. Centrifugal inertia forces regarding to planet wheel rotation around carrier center are simulated by rotation of coordinate system with center in O2 around coordinate system with center in OH.

Verification results presented in Figure 4a for three values of eccentricity ratio : 0.2, 0.4 and 0.6. Comparison of results shows good correspondence of two models. In Figure 4с the pressure distribution for two models for conditions of rotating carrier and nonrotating planet wheel (n2 = 0 rpm, nH = 6000 rpm) shows that centrifugal fluid inertia forces producing positive relative pressure in zone the most distant from carrier center and negative relative pressure in zone most close to carrier center.

Oil pressure in bearing presented in Figures 4,5 and 6 are absolute due to boundary conditions for ambient pressure taken into account. Both Reynolds and STAR-CD mathematical models obtaining in results negative absolute pressure values. Negative value of oil pressure is shown by dash line only in Figure 4 for better understanding of comparison between Reynolds and STAR-CD models. In zone where absolute pressure less then ambient pressure the cavitation effects take place and absolute pressure in this zone is not less than zero. Current models (Reynolds and STAR-CD) don't take into account discontinuous flow of fluid. However pressure in unpressurized zone gives small income to bearing carrying force and can be neglected. Thus in verificated model of journal bearing based on Reynolds equation (Figure 5) all pressures less than zero are set equal to zero.

Pressure distribution in bearing for listed above parameters for bearing with length to diameter ratio (l/d) equal to 1 is calculated for different shaft journal eccentricity in bearing. In Figures 5 and6 pressure distribution for different directions of constant shaft journal eccentricity (eccentricity ratio = 0,3) is shown. Centrifugal forces have divergent influence on total planet bearing pressure depending upon direction of bearing eccentricity related to line connected carrier and planet wheel centers and corresponding to eccentricity hydrodynamic pressure. Thus for hydrodynamic pressure concentrated in fluid film most distant from carrier center (for example: angles π/2 and π in Figures 5 and6) centrifugal forces increasing total oil pressure in bearing. For hydrodynamic pressure concentrated in fluid film most close to carrier center (for example: angles 0 and 3π/2 in Figure 5) total oil pressure decreasing. This also leads for decreasing of positive pressure zone for some eccentricity directions. In Figures 5 and6: for angle 0 pressure zone increasing, and for angle 3π/2 -decreasing. Results for pressure distribution for constant eccentricity ratio and various eccentricity directions provide variable bearing carrying force (Figure 7) and attitude angle (Figure 8). Under the bearing carrying force F the integral force of oil pressure in bearing which is equilibrating rotor reaction in bearing is represented. For full 360° bearing with smooth sliding surfaces and fixed axis the carrying force is constant for constant eccentricity. However centrifugal inertia forces action leads to cyclic change of carrying force with maximum value at angle φe = 123° and minimum value at angle φe = 295°. Maximal force value greater then carrying force in bearing with fixed axis for 35.2% and minimum value is less for 35.4%. There are two angles φe = 23° and φe = 218° for which centrifugal inertia forces have a negligible influence.

Centrifugal inertia forces provide a fixed contribution in bearing pressure for constant rotation frequencies. Centrifugal inertia forces will have a smaller influence on total pressure in case of eccentricity value growing. This is explained by growing of hydrodynamic pressure for growing eccentricity while centrifugal inertia pressure leaves constant. It is demonstrated on graph in Figure 9 where bearing carrying forces ratio (Figure 9a) and relative changing in percent (Figure 9b) for two cases of fixed bearing axis and planet wheel bearing are shown.

CONCLUSION

Developed mathematical model based on modified Reynolds equation taking into account centrifugal and Coriolis forces acting in fluid in bearing gap. This model gives ability for more accurate determination of planet wheel position in bearing and calculation of bearing carrying force depending upon load comes from gear.

The sufficient influence of centrifugal inertia forces on pressure distribution in bearing and correspondingly on carrying force and attitude angle is shown. Changing of carrying force due to action of centrifugal forces in range of eccentricity ratio values = 0.2..0.6 are in range from 35% for eccentricity ratio 0.2 to 16% for eccentricity ratio 0.6 (in percent of carrying force for fixed axis bearing, Figure 9b).

Fig. 1 .Fig. 2 .

 12 Fig. 1. Planetary gear; a) structure: 1 -sun wheel; H -carrier; 2 -planet wheel; 3 -ring wheel; b) accelerations on sliding surfaces of journal bearing

Fig. 3 Fig. 4 .

 34 Fig. 3. STAR-CD model


Hale Karakaş
email: karakashal@itu.edu.tr

Sassan Jahangiri

A S Saraç

Structure and Process Parameter Relations of Electrospun Nanofibers

Keywords: Electrospinning, Electrospun Nanofibers, Polyurethane, Electrospinning process parameters, Nanofibers Structure

Electrospinning has been a process of great interest due to its versatility and potential to be used in a wide range of applications. It is possible to produce nanofibers with diameters ranging between a few nanometers to micrometers thanks to the latest developments in electrospinning. Electrospun nanofibers promise diverse applications including biotechnology, drug delivery, wound healing, tissue engineering, microelectronics, environmental protection, energy harvest and storage due to their very large surface area to volume ratio, flexibility in surface functionalities and superior mechanical performance. This paper focuses on electrospinning process principles and relation of process parameters with electrospun polyurethane (PU) nanofiber structural properties. The electrospun PU nanofibers have been used as coating on textile fabric.

INTRODUCTION

Electrospinning is a simple and versatile technique that produces continuous micro and nano diameter polymeric fibers. Electrospun nanofibers promise diverse applications including biotechnology,drug delivery, wound healing, tissue engineering, microelectronics, environmental protection, energy harvest and storage due to their very large surface area to volume ratio, flexibility in surface functionalities and superior mechanical performance [START_REF] Huang | A review on polymer nanofibers by electrospinning and their applications in nanocomposites[END_REF][START_REF] Venugopal | Applications of polymer nanofibers in biomedicine and biotechnology[END_REF][START_REF] Wang | Functional polymeric nanofibers from electrospinning[END_REF]. There is also the advantage to control nanofiber composition and electrospinning parameters to achieve the desired property and functionality [START_REF] Bhardwaj | Electrospinning: A fascinating fiber fabrication technique[END_REF]. The ideal targets in electrospinning a polymer into nanofiber are that the fiber diameters must be consistent and controllable, uniformity of fiber diameter must be achieved, the fiber surface must be defect-free and continuos single nanofibers must be collectable.

The characteristics of electrospun nanofibers are determined by electrospinning parameters and as they effect fiber morphologies, it is very important to understand these working parameters. It is much easier and more possible to obtain desired fiber diameters and morphologies through control of these parameters.

The parameters governing electrospinning process are given in Figure 1. The effect of these parameters have been investigated widely. Sukigara et al have suggested that an optimum solution concentration must be obtained, as at very low concentrations beads are formed, whereas at very high concentrations continuous fiber cannot be obtained due to inability to maintain the flow of the solution [START_REF] Sukigara | Regeneration of bombyx mori silk by electrospinning-Part 1: processing parameters and geometric properties[END_REF]. Fong et al showed that higher polymer concentrations led to a structure with less beads [START_REF] Fong | Elastomerics nanofibers of styrene-butadiene-styrene triblock copolymer[END_REF]. Koshi et al have investigated the structure of nanofibers at various molecular weights and they found that keeping the concentration constant, using a polymer with too low molecular weight leads to formation of beads rather than fibers,whereas a very high molecular weight will result in very large nanofiber diameters [START_REF] Koshi | Effect of molecular weight on fibrous PVA produced by electrospinning[END_REF]. The effect of applied voltage has been extensively studied and there are different arguments. Reneker et al have shown that applied voltage does not have a significant effect on the nanofiber diameter in electrospinning of polyethylene oxide [START_REF] Reneker | Nanometer diameter fibers of polymer produced by electrospinning[END_REF], while other researchers observed that increase in applied voltage favoured the narrowing of fiber diameter and they showed that fiber diameter decreased with increasing voltage due to the increase in electrostatic repulsive force on the charged jet and bead formation increased [START_REF] Demir | Electrospinning of polyurethane fibers[END_REF][START_REF] Beachley | Effect of electrospinning parameters on the nanofiber diameter and length[END_REF]. Thompson et al have determined material and operating parametersby varying the parameter values in an electrospinning theoretical model and showed that volumetric charge density,distance from nozzle to collector initial jet/orifice radius, relaxation time and viscosity have the most significant effect on fiber diameter [START_REF] Thompson | Effects of parameters on nanofiber diameter determined from electrospinning model[END_REF].

Figure 1. Electrospinning process parameters

Polyurethanes (PU) are segmented polymers built up from soft and hard segments. They have a highly elastomeric behavior, abrasion and chemical resistance, clarity and tensile strength [START_REF] Jeong | Preparation of polyurethane cationomer nanofiber mats for use in antimicrobial nanofilter applications[END_REF][START_REF] Lee | Stress-strain behavior of the electrospun thermoplastic polyurethane elastomer fiber mats[END_REF].

This paper reviews electrospinning process principles, process parameters and structure and process parameters relations of electrospun nanofibers from polyurethane, by changing tip to collector distance and applied voltage. The effect of polymer solution was published elsewhere [START_REF] Karakaş | Polyurethane nanofibers obtained by electrospinning process[END_REF]. The electrospun nanofibers have been deposited on textile fabric substrate as coating.

METHOD 1.1 Electrospinning Process

Electrospinning makes use of electrostatic forces to stretch the solution or melt as it solidifies. The fiber mat is collected as a distribution of continuous nanofibers. A typical electrospinning set-up, as shown in Figure 2, consists of mainly three components : A high voltage is applied to create an electrically charged jet of polymer solution or melt. The jet undergoes stretching before it reaches the collector and it solidifies on the collector in the form of nanofibers by the evaporation of the solvent [START_REF] Wang | Functional polymeric nanofibers from electrospinning[END_REF][START_REF] Deitzel | Cotrolled deposition of electrospun poly(ethylene oxide) fibers[END_REF]. The process principle involves subjecting a polymer solution or melt held at its surface tension at the end of a capillary to an electric field. As the intensity of the electric field is increased, the hemispherical surface of the solution at the tip of the capillary elongates and forms a conical shape known as the Taylor cone. The electric field reaches a critical value where the repulsive electric force overcomes the surface tension force. At this critical value, a charged jet of the solution is ejected from the tip of the Taylor cone. The solvent evaporates as the jet travels in air. The charged polymer fiber is randomly deposited on a collector [START_REF] Doshi | Electrospinning process and applications of electrospun nanofibers[END_REF]. A number of theories and simulated modeling techniques were used to explain the electrospinning process. Generally, it is agreed that there are four different regions within electrospinning process [START_REF] Yarin | Taylor cone and jetting from lijuid droplets in electrospinning of nanofibers[END_REF][START_REF]Nanofibers and nanotechnology in textiles[END_REF] :

Materials

Thermoplastic polyurethane adhesive elastomer was supplied with a standard viscosity of about 2000 cps at 25 0 C from Coim Company. The advantages of this type of polyurethane are high adhesive strength and good flexibility, high adhesion to a range of synthetic and natural materials and good thermal resistance. PU was dissolved in Dimethylformamid (DMF, (CH3)2NC(O)H, Riedel-de Haen, analytical). All of the chemicals were used as received.

Preparation and characterization of nanofibers

For preparing electrospinning solutions, PU was dissolved in in DMF. The effect of process variables were studied and analyzed by using DMF as the solvent. The electrospinning set-up at Istanbul Technical University Polymer Science and Technology laboratory (Figure 3). The set-up consists of a syringe pump (Ne-500 model, New Era Pump Systems In., USA) with a feeding rate from 5.5 L/h to 400 mL/h, a high-voltage direct current (DV) power supplier generating positive DC voltage up to 30 kV (ES30 model, Gamma Hiigh Voltage Inc., USA). The electrospun nanofibrous web obtained was collected on a grounded collector, covered with aluminium foil. The solution was loaded into a syringe, having a needle outer diameter of 0.8 mm. A positive electrode was clipped onto the syringre needle. The feeding rate of the polymer solution was controlled by the syringe pump and the PU polymer solutions were electrospun on the collector. The electrospinning process was carried out at room temperature.

The process parameters were changed in order to see their effect on the fiber diameter, fiber diameter distribution and fiber morphology [START_REF] Jahangiri | [END_REF].

Figure 3. Schematic illustration of the nanofiber electrospinning process

Nanofiber images were taken by ZEISS, EVO MA10 model SEM. The morphology was observed with these SEM images.

RESULTS AND DISCUSSION

Electrospinning of PU nanofibers obtained by PU/DMF solution resulted in lower nanofiber diameter. The effect of process variables were studied and analyzed by using DMF as the solvent. SEM photographs of electrospun nanofbers obtained from different polymer concentration solutions, keeping other process and material parameters constant, are given in Figure 4. (Voltage 15 kV, tip to collector distance 15 cm, flow rate 0.5 mL/h). The fibers were analyzed for their diameter and morphology and the results were published elsewhere [START_REF] Karakaş | Polyurethane nanofibers obtained by electrospinning process[END_REF]. It can be observed that at very low polymer concentration, it was impossible to obtain nanofiber. As the concentration was gradually increased, nanofibers were obtained, however the bead structure was predominant in the obtained web. The number of the beads decreased as the polymer concentration was further increased, and finally a more uniform electrospun nanofiber web could be obtained at higher polymer concentration [START_REF] Karakaş | Polyurethane nanofibers obtained by electrospinning process[END_REF].

(A) (B) (C) (D) (E) (F)
Tip to collector distance has a significant effect on the fiber diameter and morphology. Figure 5 shows the SEM images and Figure 6 shows the fiber diameter distribution of electrospun PU nanofibers at various distances. cm (E) 20 cm SEM results and fiber diameter distributions showed that there is a slight decrease in fiber diameter with an increase in the number of beads. Formation of beads is an undesired ccharacteristic in nanofibers, though decrease in fiber diameter with increase in tip to colector dictance may favor some applications, where lower diameters are required. The effect of applied voltage as also studied to observe the change in nanofiber characteristics. The process parameters were kept at 10 wt% polymer solution, 15 cm tip to colector distance and 0.5 mL/h feed rate. The SEM results are given in Figure 7. The diameter range was between 221.2 nm and 506.15 nm during these trials. The average fiber diameter was 364.48 nm. Further increase in applied voltage led to a slight decrease in fiber diameter and a structure without beads. As the voltage was finally increased to 20 kV, the fiber diameter decreased, whereas a structure with beads was formed.

In order to investigate the applicability of electrospun PU nanofibers on textile fabric, the nanofibers have also been deposited on textile fabric (Figure 8 and Figure 9). The electrospinning conditions were selected as 10 wt% polymer solution concentration, 17.5 cm tip to collector distance 10 kV applied voltage, 0.5 ml/h solution flow rate.

CONCLUSION

This paper focused on electrospinning process and the parameters effective on the obtained nanofiber diameter and fibar diameter distribution. PU nanofibers were electrospun and effective parameters were determined. Fiber diameters at various tip to collector distances were measured and SEM images were analyzed. Process parameters were selected to try the deposition of PU nanofibers on fabric surface. The electrospinning process was carried out at these parameters and PU was electrospun on denim fabric for coating.

Figure 2 .

 2 Figure 2. Schematic diagram of set-up of electrospinning a)typical vertical set-up, b) horizontal set up [4]

Figure 4 .

 4 Figure 4. SEM image of nanofibers obtained from different polymer concentrations (A) 4 wt% PU, (B) 6 wt% PU, (C) 8 WT% PU (D) 9 wt% PU, (E) 10 wt% PU, (F) 12 wt% PU

Figure 5 .Figure 6 .

 56 Figure 5. SEM image of nanofibers obtained from different tip to collector distances (A) 10 cm, (B) 12,5 cm (C) 15 cm (D) 17,5 cm (E) 20 cm

Figure 7 .

 7 Figure 7. SEM image of nanofibers obtained from different applied voltages(A) 10 kV, (B) 15 kV (C) 20 kV

Figure 8 .Figure 9 .

 89 Figure 8. Deposition of PU nanofibers on denim fabric surface

The base region : the charged surface of the solution at the nozzle end,

The jet region : where the solution travels along a straight line,

The splay region : where the jet splits into many nanofibers,

The collector region : where nanofibers eventually settle.