TY  - JOUR
AU  - Lečić, Milan
AU  - Ćoćić, Aleksandar
AU  - Čantrak, Svetislav
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2443
AB  - Measuring spatial correlations of velocity is done by simultaneous measurement of velocity vector in two different measuring points. Usually, the points should be at a very small distance. While performing correlation measurements in turbulent swirling flow in the pipe, it is necessary to have very precise positioning of hot-wire probes, both by angle and distance. In this research, measurements of spatial correlations in such flow field are performed, for two different cases: velocity correlations in two points on different radial distance and in two points on different axial distance, parallel to the pipe axis. For such measurements two original devices for positioning of hot-wire probes are developed. With these devices appropriate angle positioning and radial and axial distance of hot-wire probes are achieved. Cross-correlation diagrams are also given in this article, as an illustration of capabilities of these original devices for hot-wire probes positioning.
PB  - Springer, New York
T2  - Experimental Techniques
T1  - Positioning Devices For Measuring Spatial Velocity Correlations in Turbulent Swirl Flow in the Pipe by Hot-Wire Probes
EP  - 128
IS  - 1
SP  - 121
VL  - 40
DO  - 10.1007/s40799-016-0018-8
ER  - 

@article{
author = "Lečić, Milan and Ćoćić, Aleksandar and Čantrak, Svetislav",
year = "2016",
abstract = "Measuring spatial correlations of velocity is done by simultaneous measurement of velocity vector in two different measuring points. Usually, the points should be at a very small distance. While performing correlation measurements in turbulent swirling flow in the pipe, it is necessary to have very precise positioning of hot-wire probes, both by angle and distance. In this research, measurements of spatial correlations in such flow field are performed, for two different cases: velocity correlations in two points on different radial distance and in two points on different axial distance, parallel to the pipe axis. For such measurements two original devices for positioning of hot-wire probes are developed. With these devices appropriate angle positioning and radial and axial distance of hot-wire probes are achieved. Cross-correlation diagrams are also given in this article, as an illustration of capabilities of these original devices for hot-wire probes positioning.",
publisher = "Springer, New York",
journal = "Experimental Techniques",
title = "Positioning Devices For Measuring Spatial Velocity Correlations in Turbulent Swirl Flow in the Pipe by Hot-Wire Probes",
pages = "128-121",
number = "1",
volume = "40",
doi = "10.1007/s40799-016-0018-8"
}

Lečić, M., Ćoćić, A.,& Čantrak, S.. (2016). Positioning Devices For Measuring Spatial Velocity Correlations in Turbulent Swirl Flow in the Pipe by Hot-Wire Probes. in Experimental Techniques
Springer, New York., 40(1), 121-128.
https://doi.org/10.1007/s40799-016-0018-8

Lečić M, Ćoćić A, Čantrak S. Positioning Devices For Measuring Spatial Velocity Correlations in Turbulent Swirl Flow in the Pipe by Hot-Wire Probes. in Experimental Techniques. 2016;40(1):121-128.
doi:10.1007/s40799-016-0018-8 .

Lečić, Milan, Ćoćić, Aleksandar, Čantrak, Svetislav, "Positioning Devices For Measuring Spatial Velocity Correlations in Turbulent Swirl Flow in the Pipe by Hot-Wire Probes" in Experimental Techniques, 40, no. 1 (2016):121-128,
https://doi.org/10.1007/s40799-016-0018-8 . .

TY  - JOUR
AU  - Ćoćić, Aleksandar
AU  - Lečić, Milan
AU  - Čantrak, Svetislav
PY  - 2014
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2025
AB  - In this paper, turbulent swirling flow in circular pipe is numerically investigated using OpenFOAM, an open-source computational fluid dynamics software. Flow is computed as 2-D axisymmetric, with various turbulent models, but with main accent on computations with Reynolds stress transport models. Two Reynolds stress models were used in computations: Launder-Gibson and Speziale-Sarkar-Gatski models. Previous author's experimental results are used as a validation tool for numerical computations. It was shown that standard two-equation models can not predict the flow in right manner, while the Reynolds stress models give good prediction of mean velocities. As apart of research Speziale-Sarkar-Gatski model is implemented in OpenFOAM code.
PB  - Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd
T2  - Thermal Science
T1  - Numerical analysis of axisymmetric turbulent swirling flow in circular pipe
EP  - 505
IS  - 2
SP  - 493
VL  - 18
DO  - 10.2298/TSCI130315064C
ER  - 

@article{
author = "Ćoćić, Aleksandar and Lečić, Milan and Čantrak, Svetislav",
year = "2014",
abstract = "In this paper, turbulent swirling flow in circular pipe is numerically investigated using OpenFOAM, an open-source computational fluid dynamics software. Flow is computed as 2-D axisymmetric, with various turbulent models, but with main accent on computations with Reynolds stress transport models. Two Reynolds stress models were used in computations: Launder-Gibson and Speziale-Sarkar-Gatski models. Previous author's experimental results are used as a validation tool for numerical computations. It was shown that standard two-equation models can not predict the flow in right manner, while the Reynolds stress models give good prediction of mean velocities. As apart of research Speziale-Sarkar-Gatski model is implemented in OpenFOAM code.",
publisher = "Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd",
journal = "Thermal Science",
title = "Numerical analysis of axisymmetric turbulent swirling flow in circular pipe",
pages = "505-493",
number = "2",
volume = "18",
doi = "10.2298/TSCI130315064C"
}

Ćoćić, A., Lečić, M.,& Čantrak, S.. (2014). Numerical analysis of axisymmetric turbulent swirling flow in circular pipe. in Thermal Science
Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd., 18(2), 493-505.
https://doi.org/10.2298/TSCI130315064C

Ćoćić A, Lečić M, Čantrak S. Numerical analysis of axisymmetric turbulent swirling flow in circular pipe. in Thermal Science. 2014;18(2):493-505.
doi:10.2298/TSCI130315064C .

Ćoćić, Aleksandar, Lečić, Milan, Čantrak, Svetislav, "Numerical analysis of axisymmetric turbulent swirling flow in circular pipe" in Thermal Science, 18, no. 2 (2014):493-505,
https://doi.org/10.2298/TSCI130315064C . .

TY  - JOUR
AU  - Lečić, Milan
AU  - Ćoćić, Aleksandar
AU  - Čantrak, Svetislav
PY  - 2014
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1893
AB  - Modeling of turbulent swirling FLow is a contemporary problem in FLuid mechanics. In order to make an appropriate modeling it is necessary to have reliable experimental data on instantaneous velocity field. This article presents original equipment for experimental investigation of swirling FLow in straight circular pipe. A major role in that equipment plays originally developed and unique hot-wire probe. This probe has high-spatial and temporal resolution, and it can also be used for measuring in a viscous sublayer. Together with detailed description of the probe, the original wind tunnel for hot-wire probes calibration is also presented in this article. The wind tunnel produces the jet with uniform velocity distribution and a very low level of turbulence.
PB  - Wiley-Blackwell, Hoboken
T2  - Experimental Techniques
T1  - Original Measuring and Calibration Equipment for Investigation of Turbulent Swirling Flow in Circular Pipe
EP  - 62
IS  - 3
SP  - 54
VL  - 38
DO  - 10.1111/j.1747-1567.2012.00812.x
ER  - 

@article{
author = "Lečić, Milan and Ćoćić, Aleksandar and Čantrak, Svetislav",
year = "2014",
abstract = "Modeling of turbulent swirling FLow is a contemporary problem in FLuid mechanics. In order to make an appropriate modeling it is necessary to have reliable experimental data on instantaneous velocity field. This article presents original equipment for experimental investigation of swirling FLow in straight circular pipe. A major role in that equipment plays originally developed and unique hot-wire probe. This probe has high-spatial and temporal resolution, and it can also be used for measuring in a viscous sublayer. Together with detailed description of the probe, the original wind tunnel for hot-wire probes calibration is also presented in this article. The wind tunnel produces the jet with uniform velocity distribution and a very low level of turbulence.",
publisher = "Wiley-Blackwell, Hoboken",
journal = "Experimental Techniques",
title = "Original Measuring and Calibration Equipment for Investigation of Turbulent Swirling Flow in Circular Pipe",
pages = "62-54",
number = "3",
volume = "38",
doi = "10.1111/j.1747-1567.2012.00812.x"
}

Lečić, M., Ćoćić, A.,& Čantrak, S.. (2014). Original Measuring and Calibration Equipment for Investigation of Turbulent Swirling Flow in Circular Pipe. in Experimental Techniques
Wiley-Blackwell, Hoboken., 38(3), 54-62.
https://doi.org/10.1111/j.1747-1567.2012.00812.x

Lečić M, Ćoćić A, Čantrak S. Original Measuring and Calibration Equipment for Investigation of Turbulent Swirling Flow in Circular Pipe. in Experimental Techniques. 2014;38(3):54-62.
doi:10.1111/j.1747-1567.2012.00812.x .

Lečić, Milan, Ćoćić, Aleksandar, Čantrak, Svetislav, "Original Measuring and Calibration Equipment for Investigation of Turbulent Swirling Flow in Circular Pipe" in Experimental Techniques, 38, no. 3 (2014):54-62,
https://doi.org/10.1111/j.1747-1567.2012.00812.x . .

TY  - CONF
AU  - Čantrak, Đorđe
AU  - Gabi, Martin
AU  - Janković, Novica
AU  - Čantrak, Svetislav
PY  - 2012
UR  - https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.201210237
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6349
AB  - Turbulence structure of swirling flows is being investigated in this paper, on the basis of experimental, self conducted measurements, and theoretical and numerical results. Turbulent swirling flows are extremely inhomogeneous, three dimensional and
anisotropic. The aim of this paper is to investigate significant influence of swirl onto statistical parameters and non-gradient
turbulent transfer. Contemporary optical measuring techniques two component laser Doppler anemometry (LDA) and stereo
particle image velocimetry (SPIV) have been applied
PB  - WILEY
C3  - Proceedings in Applied Mathematics & Mechanics
T1  - Investigation of Structure and Non-Gradient Turbulent Transfer in Swirl Flows
SP  - 497
VL  - 12
DO  - 10.1002/pamm.201210237
ER  - 

@conference{
author = "Čantrak, Đorđe and Gabi, Martin and Janković, Novica and Čantrak, Svetislav",
year = "2012",
abstract = "Turbulence structure of swirling flows is being investigated in this paper, on the basis of experimental, self conducted measurements, and theoretical and numerical results. Turbulent swirling flows are extremely inhomogeneous, three dimensional and
anisotropic. The aim of this paper is to investigate significant influence of swirl onto statistical parameters and non-gradient
turbulent transfer. Contemporary optical measuring techniques two component laser Doppler anemometry (LDA) and stereo
particle image velocimetry (SPIV) have been applied",
publisher = "WILEY",
journal = "Proceedings in Applied Mathematics & Mechanics",
title = "Investigation of Structure and Non-Gradient Turbulent Transfer in Swirl Flows",
pages = "497",
volume = "12",
doi = "10.1002/pamm.201210237"
}

Čantrak, Đ., Gabi, M., Janković, N.,& Čantrak, S.. (2012). Investigation of Structure and Non-Gradient Turbulent Transfer in Swirl Flows. in Proceedings in Applied Mathematics & Mechanics
WILEY., 12, 497.
https://doi.org/10.1002/pamm.201210237

Čantrak Đ, Gabi M, Janković N, Čantrak S. Investigation of Structure and Non-Gradient Turbulent Transfer in Swirl Flows. in Proceedings in Applied Mathematics & Mechanics. 2012;12:497.
doi:10.1002/pamm.201210237 .

Čantrak, Đorđe, Gabi, Martin, Janković, Novica, Čantrak, Svetislav, "Investigation of Structure and Non-Gradient Turbulent Transfer in Swirl Flows" in Proceedings in Applied Mathematics & Mechanics, 12 (2012):497,
https://doi.org/10.1002/pamm.201210237 . .

TY  - JOUR
AU  - Burazer, Jela M.
AU  - Lečić, Milan
AU  - Čantrak, Svetislav
PY  - 2012
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1584
AB  - Istraživanje strukture turbulencije je neophodno za razumevanje fizike strujno-termodinamičkih procesa u KGH sistemima. Analiza i proračun ovih sistema zasnovani su na poznavanju turbulentnog prenosa i njegovom modeliranju. S tim u vezi, u radu se analiziraju fenomeni nelokalnog prenosa impulsa i nelokalnog prenosa energije toplotom u zakrivljenim kanalima, asimetričnim mlazevima, vrtložnim tragovima i vihornom strujanju. Razmatra se fizika negradijentne turbulentne difuzije i negativne produkcije u brzinskim i temperaturskim poljima. Utvrđena je izvesna analogija između turbulentnih procesa u ovim klasama strujanja. Pomoću numeričke obrade sopstvenih eksperimentalnih rezultata izvršeno je modeliranje nelokalnog turbulentnog prenosa u vihornom strujanju.
AB  - The turbulence structure investigation is essential for understanding the physics of flow-thermodynamic processes in Heating, Ventilation and Air conditioning (HVAC) systems. Analysis and calculation of these systems are based on the knowledge of turbulent transfer mechanism and its modeling. In this regard, the paper analyzes the phenomena of non-local momentum transfer and non-local transfer of energy by heat in curved channels, asymmetric jets, wakes and swirling flow. The physics of nongradient turbulent diffusion and negative production in velocity and temperature fields are analyzed. There was a certain analogy between the turbulent processes in these classes of flow. By means of numerical processing of experimental results, modeling of non-local transport in turbulent swirling flow was conducted.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Fenomeni nelokalnog turbulentnog prenosa i negradijentne toplotne difuzije u KGH sistemima
T1  - On the non-local turbulent transport and non-gradient thermal diffusion phenomena in HVAC systems
EP  - 125
IS  - 3
SP  - 119
VL  - 40
UR  - https://hdl.handle.net/21.15107/rcub_machinery_1584
ER  - 

@article{
author = "Burazer, Jela M. and Lečić, Milan and Čantrak, Svetislav",
year = "2012",
abstract = "Istraživanje strukture turbulencije je neophodno za razumevanje fizike strujno-termodinamičkih procesa u KGH sistemima. Analiza i proračun ovih sistema zasnovani su na poznavanju turbulentnog prenosa i njegovom modeliranju. S tim u vezi, u radu se analiziraju fenomeni nelokalnog prenosa impulsa i nelokalnog prenosa energije toplotom u zakrivljenim kanalima, asimetričnim mlazevima, vrtložnim tragovima i vihornom strujanju. Razmatra se fizika negradijentne turbulentne difuzije i negativne produkcije u brzinskim i temperaturskim poljima. Utvrđena je izvesna analogija između turbulentnih procesa u ovim klasama strujanja. Pomoću numeričke obrade sopstvenih eksperimentalnih rezultata izvršeno je modeliranje nelokalnog turbulentnog prenosa u vihornom strujanju., The turbulence structure investigation is essential for understanding the physics of flow-thermodynamic processes in Heating, Ventilation and Air conditioning (HVAC) systems. Analysis and calculation of these systems are based on the knowledge of turbulent transfer mechanism and its modeling. In this regard, the paper analyzes the phenomena of non-local momentum transfer and non-local transfer of energy by heat in curved channels, asymmetric jets, wakes and swirling flow. The physics of nongradient turbulent diffusion and negative production in velocity and temperature fields are analyzed. There was a certain analogy between the turbulent processes in these classes of flow. By means of numerical processing of experimental results, modeling of non-local transport in turbulent swirling flow was conducted.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Fenomeni nelokalnog turbulentnog prenosa i negradijentne toplotne difuzije u KGH sistemima, On the non-local turbulent transport and non-gradient thermal diffusion phenomena in HVAC systems",
pages = "125-119",
number = "3",
volume = "40",
url = "https://hdl.handle.net/21.15107/rcub_machinery_1584"
}

Burazer, J. M., Lečić, M.,& Čantrak, S.. (2012). Fenomeni nelokalnog turbulentnog prenosa i negradijentne toplotne difuzije u KGH sistemima. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 40(3), 119-125.
https://hdl.handle.net/21.15107/rcub_machinery_1584

Burazer JM, Lečić M, Čantrak S. Fenomeni nelokalnog turbulentnog prenosa i negradijentne toplotne difuzije u KGH sistemima. in FME Transactions. 2012;40(3):119-125.
https://hdl.handle.net/21.15107/rcub_machinery_1584 .

Burazer, Jela M., Lečić, Milan, Čantrak, Svetislav, "Fenomeni nelokalnog turbulentnog prenosa i negradijentne toplotne difuzije u KGH sistemima" in FME Transactions, 40, no. 3 (2012):119-125,
https://hdl.handle.net/21.15107/rcub_machinery_1584 .

TY  - GEN
AU  - Benišek, Miroslav
AU  - Čantrak, Svetislav
AU  - Čantrak, Đorđe
AU  - Ilić, Dejan
AU  - Božić, Ivan
PY  - 2010
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6853
AB  - Опис: Технички проблем који се решава овом методом је обликовање контуре струјног простора тако да се у њему добија стабилно струјање без нежељених струјних ефеката, као што су секундарна струјања, одвајање граничног слоја, појава „мртве воде” и повећање хидрауличких губитака. Метод се заснива на општој једначини динамике Лагранж-Даламбером принципу виртуелног померања на флуидну средину. Наиме полазећи од Навије-Стоксове једначине уз одређене претпоставке применом принципа рада сила које делују на целокупну запремину струјног простора између граничних и контролних површина добија се услов кинетичке равнотеже струјања хомогеног флуида. За случај невискозног струјања решење проблема се своди на услов минимума интеграла дејства w струјног простора. Упрошћење струјања реалног флуида струјањем невискозног флуида има у овом случају оправдање због карактеристика струјања у проточном тракту без формирања мртве воде и зона са одлепљеним струјањем са танким граничним слојем. Поступак методе је развијен и примењен на низ случајева струјних простора, а специјално за обликовање струјног простора модела спирале Банки турбине при чему је постигнут високи степен корисности приликом моделских испитивања турбине.
T2  - Техничко решење прихваћено од стране Истраживачко-стручног већа Машинског факултета Универзитета у Београду
T1  - Метода за прорачун оптималних облика граничних површина струјног простора
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6853
ER  - 

@misc{
author = "Benišek, Miroslav and Čantrak, Svetislav and Čantrak, Đorđe and Ilić, Dejan and Božić, Ivan",
year = "2010",
abstract = "Опис: Технички проблем који се решава овом методом је обликовање контуре струјног простора тако да се у њему добија стабилно струјање без нежељених струјних ефеката, као што су секундарна струјања, одвајање граничног слоја, појава „мртве воде” и повећање хидрауличких губитака. Метод се заснива на општој једначини динамике Лагранж-Даламбером принципу виртуелног померања на флуидну средину. Наиме полазећи од Навије-Стоксове једначине уз одређене претпоставке применом принципа рада сила које делују на целокупну запремину струјног простора између граничних и контролних површина добија се услов кинетичке равнотеже струјања хомогеног флуида. За случај невискозног струјања решење проблема се своди на услов минимума интеграла дејства w струјног простора. Упрошћење струјања реалног флуида струјањем невискозног флуида има у овом случају оправдање због карактеристика струјања у проточном тракту без формирања мртве воде и зона са одлепљеним струјањем са танким граничним слојем. Поступак методе је развијен и примењен на низ случајева струјних простора, а специјално за обликовање струјног простора модела спирале Банки турбине при чему је постигнут високи степен корисности приликом моделских испитивања турбине.",
journal = "Техничко решење прихваћено од стране Истраживачко-стручног већа Машинског факултета Универзитета у Београду",
title = "Метода за прорачун оптималних облика граничних површина струјног простора",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6853"
}

Benišek, M., Čantrak, S., Čantrak, Đ., Ilić, D.,& Božić, I.. (2010). Метода за прорачун оптималних облика граничних површина струјног простора. in Техничко решење прихваћено од стране Истраживачко-стручног већа Машинског факултета Универзитета у Београду.
https://hdl.handle.net/21.15107/rcub_machinery_6853

Benišek M, Čantrak S, Čantrak Đ, Ilić D, Božić I. Метода за прорачун оптималних облика граничних површина струјног простора. in Техничко решење прихваћено од стране Истраживачко-стручног већа Машинског факултета Универзитета у Београду. 2010;.
https://hdl.handle.net/21.15107/rcub_machinery_6853 .

Benišek, Miroslav, Čantrak, Svetislav, Čantrak, Đorđe, Ilić, Dejan, Božić, Ivan, "Метода за прорачун оптималних облика граничних површина струјног простора" in Техничко решење прихваћено од стране Истраживачко-стручног већа Машинског факултета Универзитета у Београду (2010),
https://hdl.handle.net/21.15107/rcub_machinery_6853 .

TY  - CONF
AU  - Ćoćić, Aleksandar
AU  - Lečić, Milan
AU  - Čantrak, Đorđe
AU  - Čantrak, Svetislav
PY  - 2008
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6830
PB  - University of Bremen
C3  - GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 1, Proceedings
T1  - Invariant and Numerical Analysis of Turbulent Pipe Flow Subjected to Sudden Area Contraction
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6830
ER  - 

@conference{
author = "Ćoćić, Aleksandar and Lečić, Milan and Čantrak, Đorđe and Čantrak, Svetislav",
year = "2008",
publisher = "University of Bremen",
journal = "GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 1, Proceedings",
title = "Invariant and Numerical Analysis of Turbulent Pipe Flow Subjected to Sudden Area Contraction",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6830"
}

Ćoćić, A., Lečić, M., Čantrak, Đ.,& Čantrak, S.. (2008). Invariant and Numerical Analysis of Turbulent Pipe Flow Subjected to Sudden Area Contraction. in GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 1, Proceedings
University of Bremen..
https://hdl.handle.net/21.15107/rcub_machinery_6830

Ćoćić A, Lečić M, Čantrak Đ, Čantrak S. Invariant and Numerical Analysis of Turbulent Pipe Flow Subjected to Sudden Area Contraction. in GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 1, Proceedings. 2008;.
https://hdl.handle.net/21.15107/rcub_machinery_6830 .

Ćoćić, Aleksandar, Lečić, Milan, Čantrak, Đorđe, Čantrak, Svetislav, "Invariant and Numerical Analysis of Turbulent Pipe Flow Subjected to Sudden Area Contraction" in GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 1, Proceedings (2008),
https://hdl.handle.net/21.15107/rcub_machinery_6830 .

TY  - CONF
AU  - Čantrak, Đorđe
AU  - Lečić, Milan
AU  - Ćoćić, Aleksandar
AU  - Čantrak, Svetislav
PY  - 2008
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6829
PB  - University of Bremen
C3  - GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 3, Proceedings
T1  - Investigation of Structure and Statistical Properties of Turbulent Swirling Flow in a Pipe
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6829
ER  - 

@conference{
author = "Čantrak, Đorđe and Lečić, Milan and Ćoćić, Aleksandar and Čantrak, Svetislav",
year = "2008",
publisher = "University of Bremen",
journal = "GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 3, Proceedings",
title = "Investigation of Structure and Statistical Properties of Turbulent Swirling Flow in a Pipe",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6829"
}

Čantrak, Đ., Lečić, M., Ćoćić, A.,& Čantrak, S.. (2008). Investigation of Structure and Statistical Properties of Turbulent Swirling Flow in a Pipe. in GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 3, Proceedings
University of Bremen..
https://hdl.handle.net/21.15107/rcub_machinery_6829

Čantrak Đ, Lečić M, Ćoćić A, Čantrak S. Investigation of Structure and Statistical Properties of Turbulent Swirling Flow in a Pipe. in GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 3, Proceedings. 2008;.
https://hdl.handle.net/21.15107/rcub_machinery_6829 .

Čantrak, Đorđe, Lečić, Milan, Ćoćić, Aleksandar, Čantrak, Svetislav, "Investigation of Structure and Statistical Properties of Turbulent Swirling Flow in a Pipe" in GAMM 2008, Session of short communication-9: 'Turbulence and reactive flows', Location: SFG 1020, Slot 3, Proceedings (2008),
https://hdl.handle.net/21.15107/rcub_machinery_6829 .

TY  - CONF
AU  - Čantrak, Đorđe
AU  - Ilić, Jelena
AU  - Hyde, Martin
AU  - Čantrak, Svetislav
AU  - Ćoćić, Aleksandar
AU  - Lečić, Milan
PY  - 2008
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6418
AB  - Stereoscopic PIV measurements were made during experiments conducted in order to investigate the vortex core dynamics in a straight pipe. Instantaneous flow velocity field was obtained by the use of cross-correlation of laser exposed double frame records made on frame straddling CCD cameras. Swirl flow was induced by an axial fan, positioned at the straight pipe inlet. The purpose of the PIV measurements was to document the swirl flow field and its vortex core kinematics at different volume flow rates. Measurements were made in a pipe cross-section and a meridian section, having in mind intensities of axial and circumferential velocity components and significant gradient of the radial one. In order to achieve better results, seeding parameters and camera positions have been varied. Obtained qualitative and quantitative visualization and measurement results give closer insight into physics of complex flow processes in the swirl flow. In addition these results have been compared with theoretical-experimental and numerical results. Conducted analysis points out the compatibility of the investigated results. Correlation functions, probability distributions and statistical moments of the higher order, which are determined experimentally by the use of hot-wire anemometry, together with PIV results, point out, very specific phenomena and transport processes in the core region and turbulent shear flow in pipe swirl flow. Performed investigations make possible, not just testing, but also development of the new models for this class of very complex turbulent fluid flows.
C3  - ISFV 13 – 13th International Symposium on Flow Visualization, FLUVISU 12 – 12th French Congress on Visualization in Fluid Mechanics, July 1-4., Nice, France
T1  - PIV Measurements and Statistical Analysis of the Turbulent Swirl Flow Field
SP  - 183-080420
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6418
ER  - 

@conference{
author = "Čantrak, Đorđe and Ilić, Jelena and Hyde, Martin and Čantrak, Svetislav and Ćoćić, Aleksandar and Lečić, Milan",
year = "2008",
abstract = "Stereoscopic PIV measurements were made during experiments conducted in order to investigate the vortex core dynamics in a straight pipe. Instantaneous flow velocity field was obtained by the use of cross-correlation of laser exposed double frame records made on frame straddling CCD cameras. Swirl flow was induced by an axial fan, positioned at the straight pipe inlet. The purpose of the PIV measurements was to document the swirl flow field and its vortex core kinematics at different volume flow rates. Measurements were made in a pipe cross-section and a meridian section, having in mind intensities of axial and circumferential velocity components and significant gradient of the radial one. In order to achieve better results, seeding parameters and camera positions have been varied. Obtained qualitative and quantitative visualization and measurement results give closer insight into physics of complex flow processes in the swirl flow. In addition these results have been compared with theoretical-experimental and numerical results. Conducted analysis points out the compatibility of the investigated results. Correlation functions, probability distributions and statistical moments of the higher order, which are determined experimentally by the use of hot-wire anemometry, together with PIV results, point out, very specific phenomena and transport processes in the core region and turbulent shear flow in pipe swirl flow. Performed investigations make possible, not just testing, but also development of the new models for this class of very complex turbulent fluid flows.",
journal = "ISFV 13 – 13th International Symposium on Flow Visualization, FLUVISU 12 – 12th French Congress on Visualization in Fluid Mechanics, July 1-4., Nice, France",
title = "PIV Measurements and Statistical Analysis of the Turbulent Swirl Flow Field",
pages = "183-080420",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6418"
}

Čantrak, Đ., Ilić, J., Hyde, M., Čantrak, S., Ćoćić, A.,& Lečić, M.. (2008). PIV Measurements and Statistical Analysis of the Turbulent Swirl Flow Field. in ISFV 13 – 13th International Symposium on Flow Visualization, FLUVISU 12 – 12th French Congress on Visualization in Fluid Mechanics, July 1-4., Nice, France, 183-080420.
https://hdl.handle.net/21.15107/rcub_machinery_6418

Čantrak Đ, Ilić J, Hyde M, Čantrak S, Ćoćić A, Lečić M. PIV Measurements and Statistical Analysis of the Turbulent Swirl Flow Field. in ISFV 13 – 13th International Symposium on Flow Visualization, FLUVISU 12 – 12th French Congress on Visualization in Fluid Mechanics, July 1-4., Nice, France. 2008;:183-080420.
https://hdl.handle.net/21.15107/rcub_machinery_6418 .

Čantrak, Đorđe, Ilić, Jelena, Hyde, Martin, Čantrak, Svetislav, Ćoćić, Aleksandar, Lečić, Milan, "PIV Measurements and Statistical Analysis of the Turbulent Swirl Flow Field" in ISFV 13 – 13th International Symposium on Flow Visualization, FLUVISU 12 – 12th French Congress on Visualization in Fluid Mechanics, July 1-4., Nice, France (2008):183-080420,
https://hdl.handle.net/21.15107/rcub_machinery_6418 .

TY  - JOUR
AU  - Benišek, Miroslav
AU  - Čantrak, Svetislav
AU  - Nedeljković, Miloš
AU  - Čantrak, Đorđe
AU  - Ilić, Dejan
AU  - Božić, Ivan
PY  - 2006
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/601
AB  - Fluid flow in curved channels with various cross-sections, as a common problem in theoretical and applied fluid mechanics, is a very complex and quite undiscovered phenomenon. Defining the optimum shape of the fluid flow boundaries, which would ensure minimum undesirable phenomena, like "dead water" zones, unsteady fluid flow, etc., is one of the crucial hydraulic engineering’s task. Method of kinetic balance is described and used for this purpose, what is illustrated with few examples.
PB  - Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd
T2  - Thermal Science
T1  - Fluid boundaries shaping using the method of kinetic balance
EP  - 162
IS  - 15
SP  - 153
VL  - 10 (Suppl. 4)
UR  - https://hdl.handle.net/21.15107/rcub_machinery_601
ER  - 

@article{
author = "Benišek, Miroslav and Čantrak, Svetislav and Nedeljković, Miloš and Čantrak, Đorđe and Ilić, Dejan and Božić, Ivan",
year = "2006",
abstract = "Fluid flow in curved channels with various cross-sections, as a common problem in theoretical and applied fluid mechanics, is a very complex and quite undiscovered phenomenon. Defining the optimum shape of the fluid flow boundaries, which would ensure minimum undesirable phenomena, like "dead water" zones, unsteady fluid flow, etc., is one of the crucial hydraulic engineering’s task. Method of kinetic balance is described and used for this purpose, what is illustrated with few examples.",
publisher = "Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd",
journal = "Thermal Science",
title = "Fluid boundaries shaping using the method of kinetic balance",
pages = "162-153",
number = "15",
volume = "10 (Suppl. 4)",
url = "https://hdl.handle.net/21.15107/rcub_machinery_601"
}

Benišek, M., Čantrak, S., Nedeljković, M., Čantrak, Đ., Ilić, D.,& Božić, I.. (2006). Fluid boundaries shaping using the method of kinetic balance. in Thermal Science
Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd., 10 (Suppl. 4)(15), 153-162.
https://hdl.handle.net/21.15107/rcub_machinery_601

Benišek M, Čantrak S, Nedeljković M, Čantrak Đ, Ilić D, Božić I. Fluid boundaries shaping using the method of kinetic balance. in Thermal Science. 2006;10 (Suppl. 4)(15):153-162.
https://hdl.handle.net/21.15107/rcub_machinery_601 .

Benišek, Miroslav, Čantrak, Svetislav, Nedeljković, Miloš, Čantrak, Đorđe, Ilić, Dejan, Božić, Ivan, "Fluid boundaries shaping using the method of kinetic balance" in Thermal Science, 10 (Suppl. 4), no. 15 (2006):153-162,
https://hdl.handle.net/21.15107/rcub_machinery_601 .

TY  - JOUR
AU  - Benišek, Miroslav
AU  - Čantrak, Svetislav
AU  - Nedeljković, Miloš
AU  - Ilić, Dejan
AU  - Božić, Ivan
AU  - Čantrak, Đorđe
PY  - 2005
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/536
AB  - Određivanje optimalnog oblika strujnog prostora sa minimumom negativnih pojava (mrtva voda, nestacionarne pojave i dr) je vrlo važan zadatak inženjera hidrotehnike. U ovom radu se prikazuje metoda koja je zasnovana na Lagranžeovom principu virtuelnog rada. Metoda je primenjena pri oblikovanju uvodne komore Banki turbine.
AB  - Determination of the optimal flow field boundary with minimum undesirable phenomena (dead water zones, unsteady fluid flow, etc) is a very important task in hydraulic engineering. This paper presents one method based on the Lagrange’s principle of virtual work. The method was used for defining intake case of cross-flow(Bunki) turbine.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Primena Lagranžeovog principa virtuelnog rada za određivanje optimalnog oblika uvodne komore Banki turbine
T1  - Defining the optimum shape of the cross-flow turbine semi-spiral case by the Lagrange’s principle of virtual work
EP  - 144
IS  - 3
SP  - 141
VL  - 33
UR  - https://hdl.handle.net/21.15107/rcub_machinery_536
ER  - 

@article{
author = "Benišek, Miroslav and Čantrak, Svetislav and Nedeljković, Miloš and Ilić, Dejan and Božić, Ivan and Čantrak, Đorđe",
year = "2005",
abstract = "Određivanje optimalnog oblika strujnog prostora sa minimumom negativnih pojava (mrtva voda, nestacionarne pojave i dr) je vrlo važan zadatak inženjera hidrotehnike. U ovom radu se prikazuje metoda koja je zasnovana na Lagranžeovom principu virtuelnog rada. Metoda je primenjena pri oblikovanju uvodne komore Banki turbine., Determination of the optimal flow field boundary with minimum undesirable phenomena (dead water zones, unsteady fluid flow, etc) is a very important task in hydraulic engineering. This paper presents one method based on the Lagrange’s principle of virtual work. The method was used for defining intake case of cross-flow(Bunki) turbine.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Primena Lagranžeovog principa virtuelnog rada za određivanje optimalnog oblika uvodne komore Banki turbine, Defining the optimum shape of the cross-flow turbine semi-spiral case by the Lagrange’s principle of virtual work",
pages = "144-141",
number = "3",
volume = "33",
url = "https://hdl.handle.net/21.15107/rcub_machinery_536"
}

Benišek, M., Čantrak, S., Nedeljković, M., Ilić, D., Božić, I.,& Čantrak, Đ.. (2005). Primena Lagranžeovog principa virtuelnog rada za određivanje optimalnog oblika uvodne komore Banki turbine. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 33(3), 141-144.
https://hdl.handle.net/21.15107/rcub_machinery_536

Benišek M, Čantrak S, Nedeljković M, Ilić D, Božić I, Čantrak Đ. Primena Lagranžeovog principa virtuelnog rada za određivanje optimalnog oblika uvodne komore Banki turbine. in FME Transactions. 2005;33(3):141-144.
https://hdl.handle.net/21.15107/rcub_machinery_536 .

Benišek, Miroslav, Čantrak, Svetislav, Nedeljković, Miloš, Ilić, Dejan, Božić, Ivan, Čantrak, Đorđe, "Primena Lagranžeovog principa virtuelnog rada za određivanje optimalnog oblika uvodne komore Banki turbine" in FME Transactions, 33, no. 3 (2005):141-144,
https://hdl.handle.net/21.15107/rcub_machinery_536 .

TY  - JOUR
AU  - Benišek, Miroslav
AU  - Nedeljković, Miloš
AU  - Čantrak, Svetislav
AU  - Anicin, S
PY  - 2001
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/238
AB  - This paper deals with the phenomenon of swirling flows in a straight conical diffuser induced by the axial fan impeller, Numerous experiments for various swirling flows defined by the Re-number, the swirling flow parameter Omega(0) or S-0 and the similarity factor Phi(0) at the inlet cross-section were performed. On the basis of the results obtained, the average swirling flow characteristics changes along the diffuser are determined. Especially, the dependence of the flow energy loss and the Coriolis coefficient at the diffuser outlet on the swirling flow parameter are investigated.
PB  - Wiley-V C H Verlag Gmbh, Weinheim
T2  - Zeitschrift Fur Angewandte Mathematik Und Mechanik
T1  - Investigation of the swirling flow characteristics in a conical diffuser
EP  - S908
SP  - S907
VL  - 81
UR  - https://hdl.handle.net/21.15107/rcub_machinery_238
ER  - 

@article{
author = "Benišek, Miroslav and Nedeljković, Miloš and Čantrak, Svetislav and Anicin, S",
year = "2001",
abstract = "This paper deals with the phenomenon of swirling flows in a straight conical diffuser induced by the axial fan impeller, Numerous experiments for various swirling flows defined by the Re-number, the swirling flow parameter Omega(0) or S-0 and the similarity factor Phi(0) at the inlet cross-section were performed. On the basis of the results obtained, the average swirling flow characteristics changes along the diffuser are determined. Especially, the dependence of the flow energy loss and the Coriolis coefficient at the diffuser outlet on the swirling flow parameter are investigated.",
publisher = "Wiley-V C H Verlag Gmbh, Weinheim",
journal = "Zeitschrift Fur Angewandte Mathematik Und Mechanik",
title = "Investigation of the swirling flow characteristics in a conical diffuser",
pages = "S908-S907",
volume = "81",
url = "https://hdl.handle.net/21.15107/rcub_machinery_238"
}

Benišek, M., Nedeljković, M., Čantrak, S.,& Anicin, S.. (2001). Investigation of the swirling flow characteristics in a conical diffuser. in Zeitschrift Fur Angewandte Mathematik Und Mechanik
Wiley-V C H Verlag Gmbh, Weinheim., 81, S907-S908.
https://hdl.handle.net/21.15107/rcub_machinery_238

Benišek M, Nedeljković M, Čantrak S, Anicin S. Investigation of the swirling flow characteristics in a conical diffuser. in Zeitschrift Fur Angewandte Mathematik Und Mechanik. 2001;81:S907-S908.
https://hdl.handle.net/21.15107/rcub_machinery_238 .

Benišek, Miroslav, Nedeljković, Miloš, Čantrak, Svetislav, Anicin, S, "Investigation of the swirling flow characteristics in a conical diffuser" in Zeitschrift Fur Angewandte Mathematik Und Mechanik, 81 (2001):S907-S908,
https://hdl.handle.net/21.15107/rcub_machinery_238 .

TY  - JOUR
AU  - Čantrak, Svetislav
AU  - Benišek, Miroslav
AU  - Nedeljković, Miloš
AU  - Lečić, Milan
PY  - 2001
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/237
AB  - Investigation on the structure and mechanics of turbulent transport processes is difficult as the turbulent swirling flows are three-dimensional, inhomogeneous and anisotropic flows with shear. Investigations point to the existence of significant influence of swirl onto statistical parameters and non-local properties of turbulence. Physical-mathematical modelling of non-local turbulent transfer and contra-gradient turbulent diffusion in internal swirling flows is very difficult and requires research on fundamental physics of these processes.
PB  - Wiley-V C H Verlag Gmbh, Weinheim
T2  - Zeitschrift Fur Angewandte Mathematik Und Mechanik
T1  - Problems of non-local turbulent transfer modelling
EP  - S914
SP  - S913
VL  - 81
UR  - https://hdl.handle.net/21.15107/rcub_machinery_237
ER  - 

@article{
author = "Čantrak, Svetislav and Benišek, Miroslav and Nedeljković, Miloš and Lečić, Milan",
year = "2001",
abstract = "Investigation on the structure and mechanics of turbulent transport processes is difficult as the turbulent swirling flows are three-dimensional, inhomogeneous and anisotropic flows with shear. Investigations point to the existence of significant influence of swirl onto statistical parameters and non-local properties of turbulence. Physical-mathematical modelling of non-local turbulent transfer and contra-gradient turbulent diffusion in internal swirling flows is very difficult and requires research on fundamental physics of these processes.",
publisher = "Wiley-V C H Verlag Gmbh, Weinheim",
journal = "Zeitschrift Fur Angewandte Mathematik Und Mechanik",
title = "Problems of non-local turbulent transfer modelling",
pages = "S914-S913",
volume = "81",
url = "https://hdl.handle.net/21.15107/rcub_machinery_237"
}

Čantrak, S., Benišek, M., Nedeljković, M.,& Lečić, M.. (2001). Problems of non-local turbulent transfer modelling. in Zeitschrift Fur Angewandte Mathematik Und Mechanik
Wiley-V C H Verlag Gmbh, Weinheim., 81, S913-S914.
https://hdl.handle.net/21.15107/rcub_machinery_237

Čantrak S, Benišek M, Nedeljković M, Lečić M. Problems of non-local turbulent transfer modelling. in Zeitschrift Fur Angewandte Mathematik Und Mechanik. 2001;81:S913-S914.
https://hdl.handle.net/21.15107/rcub_machinery_237 .

Čantrak, Svetislav, Benišek, Miroslav, Nedeljković, Miloš, Lečić, Milan, "Problems of non-local turbulent transfer modelling" in Zeitschrift Fur Angewandte Mathematik Und Mechanik, 81 (2001):S913-S914,
https://hdl.handle.net/21.15107/rcub_machinery_237 .

TY  - JOUR
AU  - Čantrak, Svetislav
AU  - Benišek, Miroslav
AU  - Nedeljković, Miloš
PY  - 1996
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/136
T2  - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
T1  - Turbulenzstruktur und statistische eigenschaften der trennschicht in inneren turbulenten drallströmungen
EP  - 92
IS  - SUPPL. 5
SP  - 91
VL  - 76
UR  - https://hdl.handle.net/21.15107/rcub_machinery_136
ER  - 

@article{
author = "Čantrak, Svetislav and Benišek, Miroslav and Nedeljković, Miloš",
year = "1996",
journal = "ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik",
title = "Turbulenzstruktur und statistische eigenschaften der trennschicht in inneren turbulenten drallströmungen",
pages = "92-91",
number = "SUPPL. 5",
volume = "76",
url = "https://hdl.handle.net/21.15107/rcub_machinery_136"
}

Čantrak, S., Benišek, M.,& Nedeljković, M.. (1996). Turbulenzstruktur und statistische eigenschaften der trennschicht in inneren turbulenten drallströmungen. in ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 76(SUPPL. 5), 91-92.
https://hdl.handle.net/21.15107/rcub_machinery_136

Čantrak S, Benišek M, Nedeljković M. Turbulenzstruktur und statistische eigenschaften der trennschicht in inneren turbulenten drallströmungen. in ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 1996;76(SUPPL. 5):91-92.
https://hdl.handle.net/21.15107/rcub_machinery_136 .

Čantrak, Svetislav, Benišek, Miroslav, Nedeljković, Miloš, "Turbulenzstruktur und statistische eigenschaften der trennschicht in inneren turbulenten drallströmungen" in ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 76, no. SUPPL. 5 (1996):91-92,
https://hdl.handle.net/21.15107/rcub_machinery_136 .

TY  - JOUR
AU  - Benišek, Miroslav
AU  - Čantrak, Svetislav
AU  - Nedeljković, Miloš
PY  - 1988
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/109
AB  - The investigation of turbulent swirling flow has a great theoretical and practical importance because their appearance in nature and technics is very habitual. However, these investigations are very complicated on account of the very complex structure of such a flow. Generally, these flows aren't investigated and a convenient turbulent model for their prediction has yet to be found. The basic aims of this investigation are the t- epsilon -turbulent model which is used for the calculation of such a flow and some local turbulent kinetic energy observations in the point of the vortex core radius. The investigations are based on our experiments and the experiments of other authors and the results for only one representative measuring series are shown, so the deduced conclusions for others are identical with the presented one. 2 Refs.
T2  - Zeitschrift fur angewandte Mathematik und Mechanik
T1  - Theoretical and experimental investigation of the turbulent swirling flow characteristrics in circular pipes.
EP  - t282
IS  - 5
SP  - t280
VL  - 68
UR  - https://hdl.handle.net/21.15107/rcub_machinery_109
ER  - 

@article{
author = "Benišek, Miroslav and Čantrak, Svetislav and Nedeljković, Miloš",
year = "1988",
abstract = "The investigation of turbulent swirling flow has a great theoretical and practical importance because their appearance in nature and technics is very habitual. However, these investigations are very complicated on account of the very complex structure of such a flow. Generally, these flows aren't investigated and a convenient turbulent model for their prediction has yet to be found. The basic aims of this investigation are the t- epsilon -turbulent model which is used for the calculation of such a flow and some local turbulent kinetic energy observations in the point of the vortex core radius. The investigations are based on our experiments and the experiments of other authors and the results for only one representative measuring series are shown, so the deduced conclusions for others are identical with the presented one. 2 Refs.",
journal = "Zeitschrift fur angewandte Mathematik und Mechanik",
title = "Theoretical and experimental investigation of the turbulent swirling flow characteristrics in circular pipes.",
pages = "t282-t280",
number = "5",
volume = "68",
url = "https://hdl.handle.net/21.15107/rcub_machinery_109"
}

Benišek, M., Čantrak, S.,& Nedeljković, M.. (1988). Theoretical and experimental investigation of the turbulent swirling flow characteristrics in circular pipes.. in Zeitschrift fur angewandte Mathematik und Mechanik, 68(5), t280-t282.
https://hdl.handle.net/21.15107/rcub_machinery_109

Benišek M, Čantrak S, Nedeljković M. Theoretical and experimental investigation of the turbulent swirling flow characteristrics in circular pipes.. in Zeitschrift fur angewandte Mathematik und Mechanik. 1988;68(5):t280-t282.
https://hdl.handle.net/21.15107/rcub_machinery_109 .

Benišek, Miroslav, Čantrak, Svetislav, Nedeljković, Miloš, "Theoretical and experimental investigation of the turbulent swirling flow characteristrics in circular pipes." in Zeitschrift fur angewandte Mathematik und Mechanik, 68, no. 5 (1988):t280-t282,
https://hdl.handle.net/21.15107/rcub_machinery_109 .