Wyniki wyszukiwania - BazTech

1

Numerical investigations on the dynamic behaviour of a 2-DOF airfoil with application in energy harvesting system

Haniszewski Tomasz, Gąska Damian, Margielewicz Jerzy, Opasiak Tadeusz

Zeszyty Naukowe. Transport / Politechnika Śląska

|

2023

|

z. 118

77--91

EN

This article presents the basic airfoil model with two degrees of freedom - the semi-rigid model, where its forced vibrations were considered, and the exciting force is the aerodynamic force, including its periodic changes, that is, gusts. Since the phenomenological model under study has a coupled form, its versions after decoupling are presented, which has an impact on the results of the final research. The airfoil model presented in this way was shown from the application side in the system of a simple energy harvester based on a deformable beam with piezoelectric elements. The result of the simulation tests is a preliminary analysis of the possibility of using the airfoil as a vibration generator for the energy harvesting system. Along with the application of the mechanical part, a numerical simulation of the electrical part was also implemented, related to the transformation of the voltage generated by piezoelectric elements into a constant voltage signal with a connected receiver with power consumption similar to the Atmega microcontroller with battery charging.

2

Zastosowanie metody Stereo PIV do badania przemieszczeń wywołanych działaniem sił aerodynamicznych

Wodziak Waldemar, Sobczyk Jacek

Prace Instytutu Mechaniki Górotworu PAN

|

2022

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T. 24, nr 1-4

53--59

PL

W artykule przedstawiono pomiary deformacji ciała stałego będącego pod wpływem sił aerodynamicznych przy użyciu metody Stereo PIV. Jako obiekt badań wybrano fragment modelu płata lotniczego wykonanego w skali 1:72. Pomiary wykonano dla dwóch kątów natarcia oraz dwóch prędkości napływu, dla których wyznaczono kontury oraz rozkłady składowych przemieszczeń.

EN

The article presents measurements of deformation of a solid body under the influence of aerodynamic forces by means of the Stereo Particle Image Velocimetry method. A fragment of the airfoil model made in 1:72 scale was selected as the research object. Measurements were made for two angles of attack and two inflow velocities, for which contours and distributions of the component displacements were determined.

3

Inverse and direct optimization shape of airfoil using hybrid algorithm Big Bang-Big Crunch and Particle Swarm Optimization

Masoumi Heidar, Jalili Farhad

Journal of Theoretical and Applied Mechanics

|

2019

|

Vol. 57 nr 3

697--711

EN

In this paper, Big Bang-Big Crunch and Particle Swarm Optimization algorithms are combined and used for the first time to optimize airfoil geometry as a aerodynamic cross section. The optimization process is carried out both in reverse and direct directions. In the reverse approach, the object function is the difference between pressure coefficients of the optimized and target airfoils, which must be minimized. In the direct approach, three objective functions are introduced, the first of which is the drag to lift (D/L) ratio. It is minimized considering four different initial geometries, ultimately, all four geometries converge to the same final geometry. In other cases, maximizing lift the coefficient with the fixed drag coefficient constraint and minimizing the drag coefficient while the lift coefficient is fixed are defined as purposes. The results show that by changing the design parameters of the initial airfoil geometry, the proposed hybrid optimization algorithm as a powerful method satisfies the needs with proper accuracy and finally reaches the desired geometry.

4

Numerical investigation of endplates influence on the wing in ground effect lift force

Rojewski Adam, Bartoszewicz Jarosław

Journal of KONES

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2019

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Vol. 26, No. 4

205--210

EN

The article presents a comparison of the wing in ground effect magnitude of conceptual WIG craft model main characteristics for a wing with and without endplates which are also known as winglets in regular aircraft. In article, the author describes WIG effect with and WIG craft, which operates on low altitude, smaller than the length of wing chord, mostly above the water reservoir. WIG effect phenomenon is simple. The first aircraft needs to fly at adequate altitude, with a smaller distance between lower airfoil surface and ground static pressure rises, leading to rising of lift force. The main advantage of the wing in ground effect craft on regular aircraft is a much higher lift to drag ratio, also this phenomenon provides to drop in specific fuel consumption of aircraft and allows flying with heavier cargo due to higher lift force. Characteristics present in the article were designated from simulations, which were conducted in Ansys Fluent software. Results obtained for a wing with endplate in numerical analysis shows the superiority of this approach. Endplates provide to increase WIG effect by a decrease in induced drag through the move out vertices from the wing tips, which are made by differential pressure above and under the wing. As winglets in regular aircraft, endplates provide to save fuel. WIG craft does not need airports so it could be a cheap alternative for modern aircraft.

5

Numerical analysis of slots influence on wing in ground effect airfoil lift coefficient

Rojewski A., Bartoszewicz J.

Journal of Mechanical and Transport Engineering

|

2018

|

Vol. 70, No. 4

45--52

EN

The main purpose of this article was to study slots application influence on airfoil which flies in the wing in ground and description of the boundary layer with lift and drag coefficients change. The paper presents wing in ground effect creation mechanism description with automotive and aerospace examples. NACA M8 airfoil with full simulation results for angles of attack from 0° to 15°, with profile characteristics. Application of slots makes the wing in ground effect more efficient by lift coefficient rise and drop of drag coefficient. Slots prevent of boundary layer detachment and allow to fly with higher angles of attack without a stall.

PL

Głównym celem powstania tego artykułu było zbadanie wpływu użycia slotów na siłę nośną profilu lotniczego operującego w obszarze działania efektu przypowierzchniowego oraz zbadanie zmian w obszarze warstwy przyściennej, oraz siły nośnej i siły oporu aerodynamicznego profilu NACA M8, dla kątów natarcia od 0° do 15°. W artykule przedstawiono również przykłady użycia efektu przypowierzchniowego w lotnictwie i motoryzacji. Przedstawiono charakterystyki profilu NACA M8 dla badanych warunków. Zastosowanie slotów prowadzi do zwiększenia wpływu efektu przypowierzchniowego na siłę nośną profilu lotniczego przez zmniejszenie oporu aerodynamicznego oraz przez skierowanie oderwanej warstwy przyściennej ponownie na powierzchnie profilu, co pozwala na lot z większymi kątami natarcia.

6

The influence of the blades leading edge anti-erosion protection on main rotor performances

Wojtas M., Czajkowski Ł., Sobieszek A.

Journal of KONES

|

2018

|

Vol. 25, No. 2

409--414

EN

This article presents the influence of rotor blade airfoil shape on main rotor performances. In this case, we analysed the influence of anti-erosion tape, which is applied to the leading edge of the blade to protect the blades from environmental conditions. In Gyro-Tech Innovation an Aviation Company and Institute of Aviation the independent tests of helicopter and gyroplane main rotors were performed. Research includes: bench tests, on the test stand for dynamic testing of insulated rotors and tests on two flying constructions, gyroplane Cavalon produced by AutoGyro GmbH Company and ultralight helicopter Dynali H3. On the test bench, a two-blade rotor, used in ultralight and unmanned helicopters, was tested. In article, the authors present importance of the proper selection and application of anti-erosion coatings on rotor blades. Discuss the behaviour of the above-mentioned constructions with main rotor blades leading edge covered anti-erosion tape, during flight tests. The results of bench tests, including the comparison of polar curves of the main rotor with anti-erosion coating and without were also presented and discussed. In the summary of this article among others the solution of technological pocked introduced in the rotor blade, corresponding to the thickness of the anti-erosion tapes, in such way that after tape is applied it does not change the contour of the blade airfoil were presented.

7

The effect of using the Kline-Fogleman modification upon the coefficient characteristics of aerodynamic forces in the airfoil

Szczepaniak R., Bąbel R., Grzywacz A., Stryczniewicz W., Kowaleczko G.

Journal of KONES

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2018

|

Vol. 25, No. 2

349--356

EN

The wing is the main aircraft construction element, whose main task is to produce the lift, balancing the aircraft weight as well as ensuring the execution of all flight states for which the aircraft was designed. The selection of appropriate airfoils or the development of new ones is one of the most important constructions goals. As a rule, constructors aim at ensuring a sufficiently large lift with little aerodynamic drag in order to increase the scope of utility angles of attack and such shaping of these characteristics so that the aircraft performance, close to the critical angles of attack, guarantees an adequate level of safety. One of the methods of improving the aerodynamic properties of airfoils is the Kline-Fogleman modification. It involves an application of a step into the airfoil contour at a place. It enforces the creation of a swirling air stream, preventing the separation and maintaining airflow over the profile and thus the reduction of drags, as well as delaying separation. The use of this type of a solution is justified when designing unmanned aerial vehicles, of small sizes, which move with slow speeds and sometimes-large angles of attack, including those close to critical angels of attack. The Kline-Fogleman modification decreases the likelihood of aircraft stalling. The aim of this work is to present an analysis of airflow over NACA0012 airfoil with Kline-Fogleman modification. The calculations were made by solving the problem of numerical fluid mechanics. For calculations, the Comsol Maribor programme was used. The investigation focused on several different airfoil modifications (KFm-1, KFm-2, KFm-3). This enabled a selection of a solution, providing the most desirable aerodynamic characteristics.

8

Flow visualization over an airfoil with flight control surfaces in a water tunnel

Filipiak D., Szczepaniak R., Zahorski T., Bąbel R., Stabryn S., Stryczniewicz W.

Prace Instytutu Lotnictwa

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2017

|

Nr 1 (246)

63--78

EN

This paper demonstrates the feasibility of using-a water tunnel for the visualisation of flow in airfoils with flight control systems in the form of slots and flaps. Furthermore, the issue of using water tunnels for scientific and training purposes was explained. The technology of 3D printed models for practical tests in a water tunnel was also presented. The experiment included conducting flow visualisation tests for three airfoil models: with the Clark Y 11.7% as the base airfoil and the same airfoil with a slot and a flap. Moreover, a modification to dye injection system was introduced. The presented results of flow visualisation around models with the use of dye, confirmed the effectiveness of the applied methodology. The results and conclusions may be utilized to verify most flow-related issues in hydrodynamic tunnels and can also be used as a training element.

PL

W pracy przedstawiono uzasadnienie możliwości zastosowania tunelu wodnego do wizualizacji przepływu modeli profili lotniczych z mechanizacją w postaci slotów i klap. Ponadto przybliżono tematykę zastosowania tuneli wodnych w celach naukowych jak i szkoleniowych. Przedstawiono również technologię wydruku 3D modeli do testów praktycznych w tunelu wodnym. Eksperyment obejmował przeprowadzenie badań wizualizacyjnych dla trzech modeli profilu lotniczego: jako bazowy profil Clark Y 11.7% oraz ten sam profil ze slotem i z klapą. Ponadto autorzy pracy wprowadzili modyfikację wprowadzania barwnika przed badany model geometryczny umiejscowiony na trzymaku w przestrzeni pomiarowej. Przedstawione wyniki zobrazowania przepływał w:okół modeli za pomocą barwnika potwierdziły skuteczność zastosowanej metodyki prowadzenia eksperymentu na charakterystycznych kątach natarcia. Wyniki i wnioski można wykorzystać do zweryfikowania większości zagadnień przepływowych w tunelach hydrodynamicznych jak również mogą posłużyć jako element szkoleniowy.

9

Automatyzacja definiowania kształtu profili lotniczych w programie AutoCAD

Warchulski J., Warchulski M.

Mechanik

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2017

|

R. 90, nr 7

609--611

PL

Przedstawiono zastosowania systemów CAx w automatyzacji zadań graficznych. Przeanalizowano możliwość wykorzystania języka AutoLISP i środowiska Visual LISP do tworzenia kształtu profili lotniczych w systemie CAx.

EN

Possibilities of using of CAx systems to automation process of graphical tasks are presented. Possibility of using AutoLISP language with Visual LISP environment to create aerofoil shape in CAx system are analysed.

10

Numerical analysis of influence of the wing in ground effect on aircraft lift coefficient and on car downforce coefficient

Rojewski A., Bartoszewicz J.

Journal of Mechanical and Transport Engineering

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2017

|

Vol. 69, No. 2

47--55

EN

The paper presents the mechanism of the wing in ground effect formation, also shows the structure of wing in ground craft, and race car, which uses wing in ground effect. Results of numerical analysis are as expected, which means, the lift coefficient is higher for positive angles of attack, and lower for negative angles of attack. The paper details also characteristics of lift and drag coefficients in the angle of attack function. The numerical research was conduct in Ansys Fluent 15.0 academic license.

PL

W artykule przedstawiono zjawisko efektu przypowierzchniowego i powód jego powstawania. W pracy ujęto również opis konstrukcji samolotu korzystającego z efektu przypowierzchniowego jak i samochodu wyścigowego. Wyniki analizy numerycznej, tak jak przypuszczano, ukazały działanie efektu przypowierzchniowego zwiększającego współczynnik siły nośnej dla kątów natarcia większych od zera stopni oraz działanie odwrotne dla ujemnych kątów natarcia. Praca zawiera również charakterystyki przebiegu współczynnika siły nośnej i siły oporu w funkcji kąta natarcia dla badanego profilu. Analiza numeryczna została przeprowadzona w programie Ansys Fluent 15.0 academic license.

11

Design and optimisation of main rotor for ultralight helicopter

Stalewski W.

Journal of KONES

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2017

|

Vol. 24, No. 4

287--295

EN

A modern main rotor, dedicated to the ultralight helicopter, has been designed and optimised. Due to assumed simplicity of the rotor design and taking into account some technological constraints, the principal purpose of the presented research was to design a dedicated airfoil which, when applied on the main-rotor blades, would influence satisfactory improvement in a performance of the ultralight helicopter, especially in fast flight. The design and optimisation process has been supported by a computational methodology. The in-house software has been used for direct and inverse design of shapes of the rotor-blade airfoils. Aerodynamic properties of the airfoils as well as the helicopter main rotor were evaluated based on both the two-dimensional and three-dimensional flow simulations conducted using the ANSYS FLUENT software that was used to solve U/RANS equations. Based on the results of conducted computational simulations of fast flight of the ultralight helicopter, it can be concluded that the newly designed main rotor, compared to the baseline, may give certain improvement in helicopter performance in fast flight. In addition, the application of this newly designed rotor may lead to increase of a maximum speed of the helicopter flight, due to the greater lift force achievable by this rotor on the retreating blade, which is favourable from point of view of keeping of a lateral balance of the helicopter in fast flight.

12

Airfoil selection for wing in ground effect craft

Rojewski A., Bartoszewicz J.

Journal of KONES

|

2017

|

Vol. 24, No. 4

265--269

EN

The main purpose of this article was to select airfoil, which generates the biggest lift coefficient, with possibly smallest drag coefficient when the airfoil flies in the wing in ground effect. Wing in ground effect occurs in the direct proximity of ground, the article presents wing in ground effect creation mechanism description with automotive and aerospace examples. The article shows also wing in ground conditions of Ansys Fluent software simulation for all cases with conditions of analysis convergence. The article contains results of the numerical analysis for ten airfoils in three different positive angles of attack in the wing in ground flight; ten airfoils for free stream flight in the same angles of attack as in wing in ground effect, results contains lift and drag coefficients with NACA M8 airfoil presentation as authors choice for wing in ground effect crafts airfoil with full simulation results for angles of attack from –5° to 15°, with profile characteristics. The article shows physics of stall in the wing in ground effect, and a description why stall in WIG effect flight occurs only with drag coefficient rise without lift coefficient drop, and safety measures for aircraft landing with wing in ground effect influence.

13

Aerodynamic design of modern gyroplane main rotors

Stalewski W.

Prace Instytutu Lotnictwa

|

2016

|

Nr 1 (242)

80--93

EN

Process of aerodynamic design and optimisation of main rotors intended for modern gyroplanes has been presented. First stage of the process was focused on development of family of airfoils, designed and optimised especially towards gyroplane applications. In next stage, based on developed family of airfoils, two alternative gyroplane main rotors were designed. The main optimisation criterion was to minimise aerodynamic drag of the rotor, for assumed flight velocity and lift force generated by the rotor, balancing the weight of the gyroplane. The paper discusses the applied methodology of design and optimisation as well as presents geometric and aerodynamics properties of designed main rotors.

PL

Przedstawiono proces aerodynamicznego projektowania i optymalizacji nowoczesnych wirników autorotacyjnych. Pierwszy etap prac dotyczył opracowanie rodziny profili lotniczych zaprojektowanych i zoptymalizowanych specjalnie pod kontem zastosowania ich na łopatach wirnika nośnego wiatrakowca. W kolejnym etapie, w oparciu o opracowaną rodzinę profili, zaprojektowano i zoptymalizowano dwa alternatywne wirniki nośne. Głównym kryterium optymalizacji było zminimalizowanie oporu aerodynamicznego wirnika, dla zakładanej prędkości lotu i siły nośnej generowanej przez wirnik, równoważącej ciężar wiatrakowca. Omówiono zastosowaną metodykę projektowania i optymalizacji konstrukcji lotniczych, jak również przedstawiono geometryczne i aerodynamiczne własności zaprojektowanych wirników nośnych.

14

Identification of the boundary layer shock wave interaction type in transonic flow regime

Placek R., Stryczniewicz W.

Journal of KONES

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2016

|

Vol. 23, No. 2

285--292

EN

The paper presents various approaches to wind tunnel data analysis when identifying the shock wave boundary layer interaction type. The investigation was carried out in the transonic flow regime in the N-3 Wind Tunnel of Institute of Aviation. The Mach number was 0.7 and Reynolds number was approximate equal 2.85 million. The object of the research was a laminar airfoil in configuration without and with turbuliser device mounted on the upper model surface. In order to achieve turbulent boundary layer in front of the shock wave the carborundum strip was used. The effect of the varying angle of incidence on the flow filed was investigated. During experimental research, different means and test methods were applied (pressure measurements, Schlieren and oil visualisation, Particle Image Velocimetry (PIV), hot-film anemometry). The results were analysed in terms of the shock wave boundary interaction type. Most of results were in good agreement with theoretical models reported in the literature. The study showed that combination of various measurement techniques should be used in the shock wave boundary investigations in order to achieve more consistent and reliable conclusions. The results of the presented research can also be used for better understanding other mechanisms i.e. the boundary layer shock wave separation process in transonic flow regime.

15

CFD analysis of aerofoil using dimples and prevent radar signals using stealth technology

Maheswaran R., Manikandan R.

Archives of Materials Science and Engineering

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2016

|

Vol. 77, nr 2

72--77

EN

Purpose: The main objective of aircraft aerodynamics is to enhance the aerodynamic characteristics and maneuverability of the aircraft. This enhancement includes the reduction in drag and stall phenomenon. The airfoil which contains dimples will have comparatively less drag than the plain airfoil. Introducing dimples on the aircraft wing will create turbulence by creating vortices which delays the boundary layer separation resulting in decrease of pressure drag and also increase in the angle of stall. In addition, wake reduction leads to reduction in acoustic emission. The overall objective of this paper is to improve the aircraft maneuverability by delaying the flow separation point at stall and thereby reducing the drag by applying the dimple effect over the aircraft wing. Design/methodology/approach: This project includes computational analysis of dimple effect on aircraft wing, using NACA 0018 airfoil. Dimple shapes are circular which locates the inward, outward are selected for the analysis; airfoil is tested under the inlet velocity of 30m/s at different angle of attack (-5°, 0°, 5°, 10°, and 15°). Findings: This analysis favors the dimple effect by increasing L/D ratio and thereby providing the maximum aerodynamic efficiency, which provides the enhanced performance for the aircraft. Practical implications: Stealth technology is based on the principle of reflection and absorption that makes the objects’ observability lower and stealthy. A 'stealth' vehicle will generally have been designed from the motive to reduce RCS (Radar Cross Section) of aircrafts i.e. radar signature of aircrafts.

16

Obliczanie współczynnika ciągu wirnika nośnego śmigłowców

Sarnowski W., Stokfisz K.

Zeszyty Naukowe / Wyższa Szkoła Oficerska Sił Powietrznych

|

2015

|

Nr 4

147--154

PL

W artykule przedstawiono przykład możliwości autorskiego programu do obliczania współczynnika ciągu wirnika nośnego śmigłowca. Omówiono również jego przydatność w procesie dydaktycznym w Uczelniach. Oprogramowanie służy głównie do wyliczania współczynnika ciągu. W artykule zostaną również przedstawione inne możliwości programu, takie jak np. analiza doboru parametrów geometrycznych łopaty śmigłowca. Praca zawiera również algorytm obliczeniowy, wykorzystywany w programie razem z przykładem podstawowych obliczeń.

EN

The article presents the possibilities of the authors’ own program for calculating helicopter main rotor thrust coefficient. The usefulness of the program in the educational process at universities is also discussed. The software is mainly used to calculate the thrust coefficient. Other application possibilities of the program, such as the analysis of the selection of geometric parameters of helicopter blades are presented as well. The paper contains calculation algorithm used in the program together with an example of basic calculations.

17

Shock wave induced flow separation control by Air-Jet and Rod Vortex Generators

Tejero F., Doerffer P., Szulc O.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

|

2015

|

Vol. 19, No 2

167--180

EN

Flow separation control by Vortex Generators (VGs) has been analyzed over the last decades. The majority of the research concerning this technology has been focused on subsonic flows where its effectiveness for separation reduction has been proven. Less complex configurations should be analyzed as a first step to apply VGs in transonic conditions, commonly present in many aviation applications. Therefore, the numerical investigation was carried out for a Shock Wave-Boundary-Layer Interaction (SWBLI) phenomenon inducing strong flow separation at the suction side of the NACA 0012 profile. For this purpose, two kinds of VGs were analyzed: well documented Air-Jet Vortex Generators (AJVGs) and our own invention of Rod Vortex Generators (RVGs). The results of the numerical simulations based on the RANS approach reveal a large potential of this passive flow control system in delaying stall and limiting separation induced by a strong, normal shock wave terminating a local supersonic area.

18

Developing a new approach in diagnostic methods of technical state of propeller of gas pumping unit

Zamikhovskyi L., Ivanyuk N.

AGH Drilling, Oil, Gas

|

2013

|

Vol. 30, no. 2

345--351

EN

To estimate the influence of changes in aerodynamic and shape characteristics of propellers of the gas pumping unit on process variables of gas pumping unit using the mathematical modeling methods. The method theoretically based Fredholm equation of the second kind for the tangential velocity component, its computational solution, and estimation of aerodynamical characteristics of airfoil of blades in special chosen frame of reference depending on the airfoil and attack angle. For the estimation of influence of shape configuration changes, which are determined by the configuration of blades of propeller on vibration characteristics of blades, cross-sectional area of blades and its second moment the numerical methods are used. Different methods of reproducing of shape configuration of airfoil of blades using experimental data of coordinates of relevant set points of airfoil are considered. Theoretical results could be used in the research and estimation of influences of configuration blade change and quantity of strained blades on the productivity of pumping units. The conducted research and its results can be the basis of creating of new non-destructive testing methods for gas pumping units and creating a new system of control. Shown results allow increasing operational reliability of facilities that were under research and systems, which can be helpful for Ukrainian gas and oil industry facilities.

19

Wind tunnel research on the influence of active airflow on the lift force generated by the airfoil

Magryta P.

Advances in Science and Technology. Research Journal

|

2013

|

Vol. 7, nr 19

60--65

EN

The paper discusses the results of wind tunnel tests of airfoils with additional active airflow applied to their upper surfaces. These studies were carried out for a range of velocities up to 28 m/s in an open wind tunnel. Several types of airfoils selected for the examination feature different geometries and are widely applied in today’s avia¬tion industry. The changes in the lift and drag force generated by these airfoils were recorded during the study. The test bench for the tests was equipped with a compressor and a vacuum pump to enable airflow through some holes on the airfoil upper surface. A rapid prototyping method and a 3D printer based on a powder printing technique were applied to print the airfoils. All of their surfaces were subject to surface grind¬ing to smooth their external surfaces. The wind tunnel tests with and without active airflow applied to airfoils are summarised in the paper.

20

Velocity-Based Lift Coefficient Calculations

Olasek K, Karczewski M.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

|

2012

|

nr 142

7--15

EN

An innovative method for the lift coefficient calculation is presented. The algorithm used is based on Kutta-Joukowski theorem and takes advantage of the information about the velocity field around the airfoil. For the purpose of verification of the proposed method, a reference pressure-based force results for the flow simulation around NACA0012 airfoil were used.

PL

Prezentowana jest innowacyjna metoda obliczania współczynnika siły nośnej. Użyty algorytm oparto na założeniach twierdzenia Kutty-Żukowskiego wykorzystując do obliczeń informację na temat pola prędkości wokół profilu aerodynamicznego. W celu weryfikacji wyników otrzymanych dzięki proponowanej metodzie dokonano ich porównania z pomiarami sił bazującymi na rozkładzie ciśnienia uzyskanymi na drodze symulacji numerycznych opływu wokół profilu lotniczego NACA0012.