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Energy Procedía 69 (2015) 563 - 572

International Conference on Concentrating Solar Power and Chemical Energy Systems,

SolarPACES 2014

Advancing tube receiver performance by using corrugated tubes

R. Uhliga*, B. Gobereita, J. Rheinlandera

aInstitute of Solar Research, German Aerospace Centre (DLR), Pfaffenwaldring 38-40, 70569 Stuttgart, BW, Germany

Abstract

Direct introduction of solar energy into a Brayton cycle using Solar Tower systems enables a highly efficient conversion of the solar energy, especially so when combined cycles are used. One key component of such a solar gas turbine system is the receiver. High and inhomogeneous heat fluxes pose the main challenge for the design of such receivers. One possible design of the receiver uses directly irradiated metallic tubes arranged in an insulated cavity.

The paper presents the results of a study comparing thermo hydraulic absorber tube layouts with varying absorber tube dimensions and number of parallel tubes. The more parallel tubes are used the lower is the velocity of the fluid flow and in the same way the heat transfer coefficient is reduced. This leads to higher wall temperatures and therefore to a lower receiver efficiency. Using corrugated tubes instead of smooth tubes gives the possibility to increase the heat transfer coefficient. A thermo hydraulic test bench was developed in order to analyze the influence of different structures of corrugated tubes on heat transfer capability and pressure drop.

The geometry of helically ribbed tubes was optimized using CFD modelling. Design goal was a high heat transfer coefficient without exceeding the allowed pressure drop of the turbine. The resulting configurations were used to improve a tubular receiver based on the SOLUGAS receiver design.

A thermal FEM model was used to analyze the temperature field and the efficiency of the different receiver designs. Solar radiation, convection to fluid, radiation exchange, convective and conductive losses were considered in the model. It was found that the receiver efficiency of about 0.719 (at design point) could be increased up to 0.835 by using more parallel absorber tubes than needed to fulfill the pressure drop limit.

© 2015TheAuthors. Publishedby Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG Keywords: Solar tubular receiver, corrugated tubes, tethermo hydraulic test bench, CFD, FEM, thermal modelling

* Corresponding author. E-mail address: ralf.uhlig@dlr.de

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG doi: 10.1016/j.egypro.2015.03.065

1. Introduction

1.1. Solar Hybrid Systems

Introducing solar energy into the gas turbine of a solar-hybrid combined cycle offers significant advantages over other solar power plant concepts. A promising way to introduce solar power is solar preheating of the compressor discharge air before it enters the combustor of the gas turbine. In order to reach the required high temperatures, a high concentration of the solar radiation is necessary. This is achieved in a Solar Tower plant where a high number of movable mirrors ("heliostats") concentrate and aim the incoming solar radiation to a receiver on top of a tower, creating a focal spot with a diameter of only a few meters. The function of the receiver is the transfer of energy contained in the highly concentrated radiation to the heat transfer medium (pressurized air).

Nomenclature

CFD Computational Fluid Dynamics

SST Shear Stress Transport

FEM Finite Element Method

Re Reynolds number

Pr Prandtl number

Q fluid Heat flow to fluid

A Heat transfer area

atube Heat transfer coefficient

TWall Wall temperature

Tm fluid Average fluid temperature

Nu Nusselt number

% Characteristic length

X Heat conductivity

c Fluid velocity

p Density

m Mass flow

cp Heat capacity

Tout fluid Fluid temperature at outlet

Tin fluid Fluid temperature at outlet

Ap Difference pressure

p! Pressure at inlet

p2 Pressure at outlet

Ç Friction coefficient (pressure drop)

l Tube length

d Tube (inner) diameter

A! Cross section area diffusor

A2 Cross section area diffusor

f Darcy friction factor

y+ Dimensional wall distance

HReceiver Receiver efficiency

Pfiuid Heat transferred to fluid

Preceiver Total power into receiver

1.2. Receiver

The receiver is one key component of a solar tower system. For gas turbine systems, where air is the heat transfer fluid, the receiver design is restricted by the low heat transfer coefficient caused by the limited pressure drop of the gas turbine itself. Furthermore, high operating temperatures combined with inhomogeneous heat flux distribution on the receiver are obstacles preventing high receiver efficiency.

The outlet temperature is limited by the high material temperatures which, together with the location and time dependent thermal gradients, lead to a complex thermo-mechanical load.

A common way to build such a receiver is the usage of metallic tubes. Therefore such receivers are commonly located in a cavity where the heat losses are reduced by lowering the heat flux, resulting in lower temperatures on the absorber. Furthermore, the internal reflections inside the cavity homogenize the temperatures and lower the optical and infrared radiation losses.

The load situation at the absorber tubes could be improved by increasing the cavity size leading to lower and more homogenous solar fluxes. An additional effect is a higher receiver efficiency as the over temperatures at the absorber tubes are lower. However, this approach also leads to higher material costs of the receiver. Previous studies showed that for such an enhanced system the levelized costs of electricity are slightly higher despite higher receiver efficiency [5].

This paper proposes instead an increase of the receiver's heat transfer area by using a larger number of parallel absorber tubes and additionally enhancing the heat transfer by using corrugated tubes.

Within the SOLHYCO project a solar-hybrid microturbine system was developed and tested [1]. 40 metallic tubes of high temperature steel were used to preheat the working fluid of a TURBEC T100 microturbine with 100 kW nominal power and a turbine inlet temperature of around 950 °C at design point. The receiver reached an outlet air temperature of 800 °C utilizing a pressure drop of 100 mBar. Wire coil inserts where placed inside the absorber tubes in order to enhance the heat transfer. The absorber tubes reached maximum temperatures up to 900 °C.

Within the SOLUGAS project a tubular receiver heating air from 330 °C up to 800 °C with a thermal power of 3.12 MW and a pressure drop of 250 mBar was developed and successfully tested [2,3]. The receiver is a prototype (with reduced mass flow) for a commercial system using the MERCURY50 3.9 MWel turbine. The SOLUGAS receiver design is the base for the receiver designs presented within this paper.

2. Thermo hydraulic modeling of tubular cavity receiver

2.1. General

The presented receiver concepts are designed to heat the compressed air of a 3.9 MWe turbine from 330 °C up to 800 °C with a mass flow of 16 kg/s at 10 Barabs with a maximum pressure drop of 250 mBar, delivering 8.327 MWth to the turbine. Tubular headers assembled in ring-shape are used to distribute and collect the air flow. The solar radiation is absorbed at the parallel absorber tubes arranged between the headers. The absorber tubes are located inside an insulated cavity with an aperture diameter of 4 m.

The cavity has an inner diameter of 6.9 m and an insulation thickness of 0.25 m. There is a gap of 0.1 m between the absorber tubes and the cavity walls to get a more homogenous heat flux distribution on the absorber tubes by solar and infrared

radiation exchange. The basic concept is illustrated in the Fig- l Tube reaver (tew concept) following figure (Fig. 1).

2.2. Thermo hydraulic receiver design model

The allowable pressure drop of the turbine limits the possible mass flow within the absorber tubes, as pressure drop is strongly related to the fluid velocity. This limits also the possible heat transfer coefficient. The minimal required number of parallel connected absorber tubes is therefore given by the inner diameter and the length of the tubes. From a thermodynamic point of view, small diameters and short tubes would be optimal as the heat transfer ability is maximized. Furthermore, small diameters need a smaller wall thickness (resistance against pressure) and lead therefore to lower thermal gradients and finally lower material costs. On the other hand a high number of parallel tubes increase the manufacturing costs (welding of absorber tubes to the headers and other components).

A simplified EXCEL®/MATLAB® based model of the receiver was used to filter possible receiver designs by parametric variation of tube diameter and tube length. Manufacturing and material costs of the entire receiver are factored in by using specific costs. The heat transfer from the absorber tubes into the working fluid is modeled by discretizing the absorber tubes into a large number of segments along the flow direction resulting in a one-dimensional approximation. Heat transfer into the fluid is calculated using Gnielinski Nusselt correlations found in [5] at each discrete segment using temperature dependent fluid properties. A homogeneous heat flux distribution is assumed along the entire tube. The pressure drop of absorber tube, headers, inlet and outlet is calculated using Reynolds correlations from [6]. The wall thickness of the tubes and headers are determined by an empiric formula for pressure-vessels found in [7].

2.3. Results of parameter study

The diagram in Fig. 2 shows the specific costs of the receiver for a variation of both inner diameter and length. The number of parallel tubes was thereby chosen to be the minimal required number of parallel tubes that would fulfill the pressure drop limit. It can be seen that there is a strong influence of the inner diameter on the total costs caused by higher manufacturing costs. Furthermore, the costs increase with longer tubes, caused by both the higher material costs and the increased number of parallel tubes (in order to keep the pressure drop below the limit). The diagram in Fig. 3 shows the maximum tube wall temperatures of the absorber tubes depending on the geometric variations. It can be seen that in principle smaller diameters result in lower material temperatures. The reason is the increased heat transfer capability due to the smaller hydraulic diameter. Longer absorber tubes in principle signify a larger heat transfer area. This results in a lower heat flux and consequently, the maximum tube wall temperature is lower. The simplified model used in this study applies a homogenous heat flux along the circumference of the absorber tubes. In reality the flux distribution in the receiver is very inhomogeneous. Therefore, the resulting maximum tube temperature results should be considered cautiously. Nevertheless, the results can help to filter designs which will not work because their material temperature is already too high. As a good compromise between costs and tube temperature an inner diameter of 30 mm and a tube length of 6 m was chosen for further investigations.

Fig. 2: Specific costs receiver designs

Fig. 3: Maximal tube wall temperatures

So far all designs assume that the best results are obtained by choosing the number of parallel absorber tubes in that way that only minimal required parallel absorber tubes are used. That means the fluid velocity and following the heat transfer coefficient is the maximal possible value. In other words, the pressure drop defines the heat transfer coefficient and the size of the absorber area.

Using more parallel tubes instead would increase the heat transfer area and could thus have a positive effect on the receiver efficiency. On the other hand the fluid velocity and therefore the heat transfer coefficient will be lower, leading to higher wall temperatures. However, lower fluid velocity also leads to a decreased pressure drop. This gives the opportunity to use the pressure drop margin to enhance the heat transfer by using corrugated tubes.

2.4. Heat transfer enhancements

To enhance the heat transfer coefficient in tubes for turbulent flows different concepts are known in literature. For turbulent flows it is effective to mix only the viscous boundary layer. Any type of insert that mixes the core flow (twisted tape, mesh or brush inserts) will not significantly enhance the heat transfer in a turbulent flow, but the pressure drop. For turbulent flows tubes with wire coil inserts, internal fins (straight or helical fins) and integral roughness (helical ribs, wire) are recommended [8,9]. The heat transfer and pressure drop correlations applicable to tube receiver designs presented in this paper have to be valid for 104 < Re < 106 and Pr about 0.7. Experimental results are available for tubes with wire coil insert. Garcia et al. presented experimental results for water and water-propylene glycol and proposed correlations for Reynolds numbers from 80 to 90'000 and Prandtl numbers from 2.8 to 150 [13]. Zhang et al. provided experimental data for turbulent air flow and correlations for the Nu number and the friction factor for Reynolds numbers between 6-103 to 1-105 [10]. The enhancement of heat transfer in the test range was between 150 % and 315 % and the friction factor was increased between 185 % and 820 %.

The heat transfer of the tubular air receiver of the SOLHYCO project was enhanced using a wire coil insert [2]. The wire coil was manufactured specifically for this receiver. An additional effort was the correct placement of the wire coil in the absorber tubes. Besides this amount of work the correct position of the wire coil cannot be checked easily after installation. Furthermore, there is no defined connection between tube wall and wire coil leading to swinging problems in operation.

A similar but much easier way to manufacture a similar structure is to use helical ribs mechanically rolled from the outside into the tube walls. The manufacturing of such structures is fast and simple and does therefore not lead to significantly higher costs of the tubes. Another advantage of this structure is that it also increases the heat transfer area as the ribs are involved in the heat transfer.

Fig. 4 shows an example of a helically ribbed tube. The geometry can be described with the diameter and the pitch of the ribs.

Fig. 4: Helical ripped tube

3. Development of a thermo-hydraulic test bench

3.1. General

The absorbed solar radiation is transferred to the fluid flow in the absorber tubes by forced convection the heat flow can be calculated with equation (1).

Qfluid ~ A ' atube ' ^fwall ~ Tm, fluid )

Therefore

The heat flow Q is depending on the heat transferring area A, the heat transfer coefficient atube and the temperature difference between the tube wall and the mean fluid temperature. The heat transfer coefficient cannot be measured directly but calculated with equation (2) and empirically determined Nusselt correlations.

Nu =— (2)

Nusselt correlations exist for smooth and rough tubes and for several corrugated tubes. Presently, no sufficient correlations exist for the structure of helical ribs and for the characteristic fluid flow in the presented solar receiver concepts. For this reason a test bench was developed to measure the thermo hydraulic characteristics of fluid flow in tubes for different tube geometries. The typical fluid flow in solar air receivers under pressure is characterized by fluid temperatures between 300 - 800 °C, Reynolds numbers between 104 < Re < 106 and pressures between 4 - 16 Bar . Measurements under these conditions are rather complex due to the high temperatures and pressure. Furthermore, the pressurized systems require a closed loop with back cooling of the heated fluid. Last but not least the high temperatures invoke uncertainty of the measurements due to heat flow by radiation and conduction to other components or to ambient. For this reason the test bench uses the law of similarity of fluid flows.

The Reynolds number is an important similarity size in the fluid mechanics. The Reynolds number describes the flow characteristic due to the influence of inertia and viscosity of the fluid. In the experimental technique the Reynolds law allows the free choice of model size, the velocity and the fluid properties, if the Reynolds number of the model and the real flow are identical [11, p86]. This allows operating under ambient pressure and moderate temperatures.

The Reynolds number can be calculated with equation (3):

Re = (3)

The heat transfer coefficient a and corresponding Nusselt number for constant wall temperature can be calculated from the heat flow Q with equation (4). Q is then depending on the temperature difference between the inlet and the outlet of the fluid flow, the average specific heat capacity cp and the mass flow m of the fluid.

O = m ■ c 4t - T ) (4)

fluid p V out, fluid in, fluid /

3.2. Test bench

The test bench uses condensing steam at the outside wall of the measured tubes. In comparison to heat transfer by forced convection of gaseous fluids the heat transfer of condensing fluids is several magnitudes higher and so a constant wall temperature can be guaranteed. For ambient pressure the tube wall temperature is then 100 °C.

The steam is constantly produced by a boiler element located in a water tank. The fluid flow through the tube is fed by an electronically speed controlled compressor. Adjacent to the compressor, fluid temperature and static pressure are measured in a tube section with larger diameter than the measured tube (to keep the dynamic pressure low). The fluid flow is then accelerated by a converging nozzle and enters the steam zone.

A converging nozzle at the end of the steam zone converts the dynamic pressure to static pressure again. The larger diameter of the adjacent tube keeps the dynamic pressure low. At this section static pressure and the fluid temperature is measured. To avoid measurement errors by heat conduction the outlet section is insulated. A special thermal barrier between inlet, outlet and steam zone reduces heat conduction between these sections. With the help of exchangeable sockets tubes with different outer diameter and a total length of 1,100 mm can be installed. The heat transferring length of the test tube in the steam zone is 1m. The test bench is designed to run in full automatic mode. A LabVIEW®-application is used to set up the measurement job.

The Reynolds number range and the intermediate steps can be defined as the base. Furthermore, the lapse of time for steady state conditions and the number of measurement repetitions can be set.

After starting the measurement, the LabVIEW®-application starts at the lowest mass flow. After the steady state conditions are reached, all measurement data are saved and the next mass flow point is piloted. The measurement is stopped automatically in case of problems like low water level at the water tank. Normally, every measurement is repeated several times to average the results. Fig. 5 shows the schematic of the test bench.

Fig. 5: Thermo hydraulic test bench

3.3. Validation

To validate the thermo-hydraulic test bench, measurements with smooth tubes have been performed. The measured data was evaluated and compared with correlations from literature. The pressure drop was determined by the difference of the (static) pressure between the inlet and outlet tube. Even if the diffusor and converging nozzle reduces the dynamic pressure there is still an additional pressure drop caused by these components.

Therefore, these additional pressure drops must be subtracted to get the pressure drop caused by friction in the measured tube. The theoretical pressure drop was calculated with the following correlations [6]:

Inlet, test tube, outlet:

A f- l P' C 2

Ap = pj -p2 = £• — •-

Converging nozzle:

^Pconverging _ nozzle

Diffusor:

= 0.04

diffusor

V A2 J

P-ci 2

The determination of the coefficient C, depends on the Re number:

Re < 2,320

0.3164

2,320 < Re < 10,000

Re > 10,000

^ = (1.8 • log Re-1.5)"

(8) (9)

The temperatures have been measured with resistor-type thermometer in the inlet and the outlet flow, two in each case. In addition, the surface temperatures of the converging nozzle and diffusor have been measured by surface thermocouples. The latter temperatures have been used to assess the over prediction of the heat transfer into the air because of heat conduction to these components. Experiments showed that the heat conduction is less than 6 % for Re=10'000 and decreases to 2.5 % at Re=100'000.

The theoretical heat transfer was determined with the experimentally measured temperatures, the mass flow and averaged properties for the air. The theoretical heat transfer was calculated with the correlations (1,2,11,12) [12]:

4 u w „ Re- 2,300

2,300 < Re < 104 NuLT = (1 -/)■ NuL +y NuT y = ^ _ 2 300 (11)

(/ /8)-Re- Pr w

104 < Re <106 NU = 1 +12.7f .(Pr--1) f = (079'lnRe"164)"2

For fully turbulent flows (Re > 104), no general expressions for entrance length for turbulent flow are available. Incropera assumes fully developed flow at x/D > 10 [12]. In the experiments the length of the inlet tube and converging nozzle is 0.3 m and therefore x/D ~15.

4. CFD Modelling

4.1. General

Even if the thermo hydraulic test bench enables an automatic measurement of different tubes (and different geometries of the inner structure), the measurements are still time consuming as high accuracy needs more than 2h for every measuring point. This and the additionally necessary repeating measurements (for averaging results) means that one measurement campaign takes about 4-6 days. Furthermore, any variation needs the manufacturing of the specific tube. In the case of the helical ribs, special tooling for every geometric variation is necessary. The strength of CFD simulations is the freedom in designing the geometry for the simulation. Parametric geometry and mesh generation allows easy and fast variations. Once the model is validated, CFD can be used for optimizing the geometry of the structures in an efficient way.

All CFD models used base on the same following model parameters. Air as ideal gas under ambient pressure was used for the fluid properties. A mass flow was defined at the inlet, ambient pressure at the outlet. A fixed homogenous wall temperature was defined at the fluid wall (the tube itself was neglected) and a rough wall with a sand grain roughness of 1-10-5 m was modelled. A mesh study was performed to guarantee the independency of the results from the discretization. As heat transfer plays a significant role the dimensionless wall distance (y+) was kept at a value of about one. The SST turbulence model was used to solve the fluid dynamics. For tube geometries producing a swirly fluid flow, the curvature correction option was additionally used to capture the rotation of the fluid more exactly.

4.2. Validation with smooth tube

As a first step the CFD model was set up for a smooth tube. The same geometry and test conditions as used for the test bench validation were used to compare the results. Fig. 6 shows the Nusselt number depending on the Reynolds number.

It can be seen that the results fit very well within the Reynolds number range of interest (20'000-60'000). The comparison of the pressure drop (Fig. 6) shows the same very good agreement between measurement, analytic solution and CFD model. In the next step, one corrugated tube which was measured at the test bench was modelled in the same way as the smooth tube and so the CFD models could be validated.

Nusselt number

■^Measurement ^Analytical CFD

0 20'000 40'000 60'000

Reynolds number

Pressure drop

^Measurement ^Analytical CFD

40'000 60'000

Reynolds number

Fig. 6: Comparison measurement, analytic and CFD results (Nusselt number, pressure drop) for a smooth tube

80'000

20'000

80'000

5. Comparison of different receiver designs

5.1. Thermal model

To evaluate the efficiency of the receiver, a thermal FE model was used. As the absorber tubes are located in a cavity, radiative exchange between absorber tubes, cavity walls and ambient follows the rules of reflection and absorption. The model considers this using a ray-tracing based algorithm for the solar wavelength. The code uses the geometric data and the optical properties of each FE of the mesh to calculate the expected heat flux distribution considering direct absorption as well as grey diffuse solar radiation exchange. The solar field consists of 151 Heliostats each with a reflecting area of 120 m2. The receiver is located on top of a 60m high tower with an elevation angle of 35 ° against the horizon. The solar heat fluxes were calculated for Seville, at March 21th 12:00 A.M. (design point). The absorber is modeled with an absorptivity of 0.9 and the cavity with an absorptivity of 0.3.

The heat transfer to the working fluid is modeled using one-dimensional fluid-flow elements. They consider heat and mass transfer of the fluid using temperature dependent fluid properties and a heat transfer coefficient from Nusselt correlations for smooth and corrugated tubes. The Nusselt number for the helically ribbed tubes was determined using the CFD model. Therefore the ideal configuration of rib diameter and pitch was found by optimizing the Nusselt number. Following the geometry of the ribs is different for the different receiver versions.

At the infrared wavelength the radiation exchange is modeled using the radiosity method of the FEM code. The heat losses by convection to ambient are considered, using a heat transfer coefficient and the ambient temperature as bulk temperature, which is estimated using a Nusselt correlation at the inner area of the cavity. Finally, the conduction losses through the insulated cavity are modeled as a heat flow at the outside walls of the cavity.

6. Results

Based on the tube dimensions defined in (2.3) several tube receivers were simulated using the thermal FEM model. Besides the maximum and average tube wall temperatures, the receiver efficiency was evaluated in order to compare the different variations. P

_ fluid

'H receiver p (13)

receiver

Fig. 7 shows the FEM results for the analyzed configurations. It can be seen that the maximum tube wall temperatures and also the average tube wall temperatures are significantly lower for designs using corrugated tubes. This leads to a significant increase of the receiver efficiency. The receiver efficiency can be increased from 71.9 % for 120 parallel smooth tubes up to 83.5 % using 400 parallel corrugated tubes. Using more parallel tubes clearly increases the costs of the receiver. The specific receiver cost of the presented design rises linear from 115 €/kWth for 120 parallel tubes up to 177 €/kWth for 400 parallel tubes. An efficiency of 80.4 % could be reached with 250 parallel corrugated tubes, leading to receiver costs of 132 €/kWth. An efficiency of 82% can be reached with 250 parallel tubes at receiver costs of 147 €/kWth.

Tube wall temperature

Max. temperature smooth tube Max. temperature helical ribs ^^ Average temperature smooth tube

;e temperature he cal ribs

200 250 300

Number of paralell tubes

Fig. 7: FEM results of maximal tube wall temperatures and receiver efficiency depending on number of parallel tubes

7. Conclusions

Using corrugated tubes can add an additional degree of freedom to the design of tubular receivers. The decrease of the heat transfer coefficient when using more parallel tubes can be compensated by influencing the turbulent flow. A thermo hydraulic test bench and CFD simulations were used to find optimal dimensions for helical ribs. It could be shown that the receiver efficiency could be increased from 71.9 % up to 83.5 % with a thermal FEM model considering all relevant thermo hydraulic boundaries of a tubular receiver for air pre heating.

References

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[3] Roman Korzynietz, Manuel Quero, Ralf Uhlig SOLUGAS - Future solar hybrid technology, Solarpaces 2012, Marrakech, Marocco

[4] R. Uhlig, et al., Strategies enhancing efficiency of cavity receivers. SolarPACES 2013, Las Vegas, USA, (2013)

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[8] Webb, R.L.; Eckert, E.R.G.; Goldstein, R.J.: Heat Transfer and Friction in Tubes with Repeated-Rib Roughness, Int. J. Heat and Mass Transfer, Vol. 14, S. 601-617, 1971

[9] Zhang,Y.F.; Liang, Z.M.; 1991. "Heat transfer in spiral-coil-inserted tubes and its application", in Advances in Heat Transfer Augmention, M.A. Ebadin, D.W. Pepper and T.Diller, Eds.,ASME Symp. Vol. HTD, 169, 31-36.

[10] Sigloch, Herbert: Technische Fluidmechanik. 8th Edition Berlin Heidelberg: Springer, 2012.- ISBN 978-3-642-22844-5

[11] Incropera, Frank P.; DeWitt, David P.; Bergman, Theodore L.; Lavine, Adrienne S.: Fundamentals of Heat and Mass Transfer. 6. Auflage USA: Wiley, 2006.- ISBN 978-0-471-45728-2

[12] Alberto Garcia, Pedro G. Vicente, Antonio Viedma: Experimental study of heat transfer enhancement with wire coil inserts in laminartransition-turbulent regimes at different Prandtl numbers, International Journal of Heat and Mass Transfer 48 (2005) 4640-4651