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1

Application of the diagnostic plot in estimation of the skin friction in turbulent boundary layer under an adverse pressure gradient

Niegodajew P., Dróżdż A., Elsner W.

Archives of Mechanics

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2021

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Vol. 73, nr 2

201--215

EN

The paper concerns the problem of determining friction velocity in wallbounded flows affected by an adverse pressure gradient (APG). In the work of Niegodajew et al. [22] the corrected Clauser chart method (CCCM) for such flow conditions was proposed. This approach utilises the mean velocity profiles and turbulence intensity profiles to accurately estimate the friction velocity. In another work, Drózdz et al. [27] presented a modified version of the diagnostic-plot scaling (DPS) which allows for direct reconstruction of turbulence intensity profiles based on the local mean velocity profile, even when the flow is affected by a strong pressure gradient. This paper is aimed at verifying whether, when combining both of these methods (i.e. DPS and CCCM), the friction velocity can be accurately determined for APG flow conditions and one can possibly take advantage from both methods. The analysis revealed that the new approach is able to predict the friction velocity with uncertainty less than 5% for all the considered cases for the Clauser–Rotta parameter β < 17. Lastly, DPS-CCCM was also confronted with two empirical approaches (from available literature) allowing for estimation of the friction velocity under APG conditions. The performance of DPS-CCCM was found to be better than the ones of two other empirical approaches.

2

Skin friction estimation in a strong decelerating flow

Dróżdż A., Elsner W., Sikorski D.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 2

365--376

EN

The paper presents the analysis of the turbulent boundary layer developed on a flat plate subjected to an Adverse Pressure Gradient (APG) and approaching separation. The aim of the study is to examine the effects of pressure gradient on a non-equilibrium boundary layer while indicating local areas of the equilibrium flow. The emphasis is on the analysis of mean flow velocity and the estimation of skin friction. It is known that accurate measurements of skin friction were considered as a difficult and demanding task despite of various measuring techniques available. A great challenge is especially the measurement of a strong decelerated turbulent boundary layer because of low shear stress and possible large measuring errors. To date, the oil film or oil drop interferometry technique, because of its high accuracy, has become a basis of turbulent-boundary-layer research. In our research, this technique has been used as a reference method for comparing with the traditional Clauser chart method, which generally is considered as not suitably for non-canonical flows. In the paper, however, a correction of the method is proposed, which allows one to increase its range of applicability. This corrected Clauser chart method (CCCM) involves only one iteration while other proposed in the literature methods employ a twofold iterative procedure. The comparison of the methods for the non-canonical turbulent boundary layer, i.e. adverse pressure gradient with a strong flow history effect has been presented. It has been shown that CCCM can be successfully used for small and medium pressure gradients, where the Clauser-Rotta pressure gradient parameter β does not exceed level close to 11.

3

The Effect of Angle of Attack and Flow Conditions on Turbulent Boundary Layer Noise of Small Wind Turbines

Afanasieva N.

Archives of Acoustics

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2017

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Vol. 42, No. 1

83--91

EN

The article aims to solve the problem of noise optimization of small wind turbines. The detailed analysis concentrates on accurate specification and prediction of the turbulent boundary layer noise spectrum of the blade airfoil. The angles of attack prediction for a horizontal axis wind turbine (HAWT) and the estimation based on literature data for a vertical axis one (VAWT), were conducted, and the influence on the noise spectrum was considered. The 1/3-octave sound pressure levels are obtained by semi-empirical model BPM. Resulting contour plots show a fundamental difference in the spectrum of HAWT and VAWT reflecting the two aerodynamic modes of flow that predefine the airfoil self-noise. Comparing the blade elements with a local radius of 0.875 m in the HAWT and VAWT conditions the predicted sound pressure levels are the 78.5 dB and 89.8 dB respectively. In case of the HAWT with predicted local angle of attack ranging from 2.98º to 4.63º, the acoustic spectrum will vary primarily within broadband frequency band 1.74–20 kHz. For the VAWT with the local angle of attack ranging from 4º to 20º the acoustic spectrum varies within low and broadband frequency bands 2 Hz – 20 kHz.

4

On the turbulent boundary layer of a dry granular avalanche down an incline. II – closure model and numerical simulations

Fang C.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 4

1245--1256

EN

Dynamic responses of the closure relations, specific turbulent Helmholtz free energy and turbulent viscosity are postulated followed by experimental calibrations. The established closure model is applied to analyses of a gravity-driven stationary avalanche with incompressible grains down an incline. While the mean velocity and volume fraction increase from their minimum values on the plane toward maximum values on the free surface exponentially, two-fold turbulent kinetic energies and dissipations evolve in a reverse manner. Most two-fold turbulent kinetic energies and dissipations are confined within the thin turbulent boundary layer immediately above the plane, with nearly vanishing two-fold turbulent kinetic energies and finite two-fold turbulent dissipations in the passive layer. The two layers are similar to those of Newtonian fluids in turbulent boundary layer flows, and are preferable recognized by the distributions of turbulent kinetic energies and dissipations.

5

Analysis of hot-wire measurements accuracy in turbulent boundary layer

Dróżdż A., Elsner W.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2014

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nr 145

39--40

EN

The paper discusses the problem of measuring velocity fluctuations of turbulent boundary layer using hot-wire probes. The study highlighted the problem of spatial resolution, which is essential when measuring small-scale in wall-bounded flows. Additionally, the attention was paid to the inconsistency in streamwise fluctuation measurements using single and X-wire probes. To clarify this problem the energy spectra using wavelet transformation were calculated. The analysis was performed for turbulent boundary layer flow, which was characterized by the Reynolds number based on the friction velocity equal ReƮ≈1000.

6

Comparison of single and X-wire measurements of streamwise velocity fluctuations in turbulent boundary layer

Dróżdż A., Elsner W.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 2

499--505

EN

The paper discusses the problem of measuring velocity fluctuations of a turbulent boundary layer using single and X-wire probes. It seems that the difference between the streamwise fluctuating component of these two probes results not only from spatial resolution, but also from influence of the wall-normal fluctuating component, which is usually not considered. It was shown that the vector summing these two components obtained from X-wire probe gives the shape of fluctuation distribution obtained from a single-wire probe. It implies that the underestimation of the near-wall peak of streamwise fluctuating component in X-wire measurements results from disregarded wall-normal fluctuations, which is obviously taken in the case of a single-wire probe. Moreover, it was shown that the criteria for wire length i.e. l+ ≤ 20 could not be sufficient to properly estimate the streamwise and wall-normal fluctuations.

7

Czynniki wpływające na deformację warstwy przyściennej przy statycznym przepływie powietrza nad złożem porowatym oraz ich wpływ na prędkość poślizgu. Część I: Turbulentna warstwa graniczna w sąsiedztwie ścianek chropowatych

Sławomirski M. R., Skotniczny P.

Prace Instytutu Mechaniki Górotworu PAN

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2012

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Vol. 14, no. 1-4

165--177

PL

W artykule autorzy rozważają wpływ nierówności powierzchni na rozkład prędkości i własności turbulentnej warstwy granicznej. Omówiono wielowarstwowy model warstwy granicznej. Jeśli wysokość nierówności nie przekracza grubości podwarstwy lepkiej, wówczas chropowatość nie wpływa na obraz ruchu turbulentnego. W przeciwnym przypadku profil prędkości zostaje zmodyfikowany, a równania go wyrażające muszą być zmodyfikowane poprzez wprowadzenie tzw. funkcji chropowatości oraz ewentualnie tzw. funkcji śladu. Przedstawiono wyniki pomiarów wyrażających zależność prędkości uśrednionej, fluktuacji prędkości oraz naprężeń turbulentnych Reynoldsa od bezwymiarowej odległości od ścianki. Pokazano, że własności przepływu turbulentnego zależą nie tylko od skali ale i od geometrii nierówności powierzchni. Czynniki te nie zawsze mogą być w prosty sposób sprowadzone do zastępczej chropowatości piaskowej. Zależność funkcji chropowatości od zredukowanej skali chropowatości przedstawiono w postaci formuły analitycznej oraz w formie grafi cznej. Zaproponowano postać równań, które opisują rozkład prędkości średniej w turbulentnej warstwie granicznej w pobliżu chropowatej a zarazem przepuszczalnej ścianki z uwzględnieniem efektów przesunięcia (ang. velocity shift) i poślizgu (ang. velocity slip).

EN

In the paper the autors discuss the influence of surface roughness on the mean velocity profi le and properties of the turbulent boundary layer. The multi-strata model of the turbulent boundary layer has been discussed. When roughness height does not exceed the thickness of the viscous sublayer, the wall roughness does not influence on the turbulent flow. In the opposite case the velocity profi le is modified. The equations expressing the mean velocity profile may then be modified by means of introduction of the roughness function and wake function. The results of measurements concerning the dependence of reduced mean velocity, velocity fluctuations, and Reynolds stress on the distance from the wall have been presented in the graphical form. It is shown that the turbulent flow properties depend explicitly on roughness geometry which in many situations cannot be reduced to the sand roughness. The dependence of the rougness function on the reduced roughness scale has been expressed in the analytical and graphical forms. The equations which describe the average velocity profile for turbulent boundary layer in the vicinity of rough and permeable wall involving the shift and slip phenomena have been proposed.

8

Application of VITA technique for detection of the organized structures present in a turbulent boundary layer under an adverse pressure gradient

Dróżdż A., Elsner W., Drobniak S.

Archives of Mechanics

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2011

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Vol. 63, nr 2

183-199

EN

The paper concerns experimental investigations of turbulent boundary layer (TBL), developing on a flat plate at Reynolds number based on momentum thickness= 3000 under an adverse pressure gradient (APG) corresponding to the case of pressure variation at axial compressor blading. In particular, the paper deals with the analysis of bursting phenomena and coherent structures activity in TBL with the use of VITA technique. The interpretation of coherent structures was based on the analysis of conditionally averaged traces of u and v velocity components recorded by X-wire probe in several boundary layer regions. The paper describes the modification introduced into the VITA method, which enables to distinguish four types of coherent structures. This modification relies on the detection of instantaneous positive or negative gradients of u and v velocity traces. It was found that bursting process under the influence of adverse pressure gradient is damped near the wall and this phenomenon is even more pronounced in the outer region of turbulent boundary layer. Furthermore, the paper gives the consistent proof, that vortices developing in TBL create the effect of bursting present in velocity signal.

9

LES of Converging-Diverging Channel Flow with Separation

Kuban L., Elsner W., Tyliszczak A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2010

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Vol. 14, No 3

283-295

EN

The paper presents the results of LES simulation of two different turbulent channels with inlet conditions corresponding to the Reynolds number Re =395. In both cases a varying pressure gradient was obtained by an adequate curvature of one of the walls. The first case is treated as a benchmark and is used to validate the numerical procedure. This case is characterized by the same cross-section area at the inlet and outlet and a bump of a smooth profile located on one of the walls designed to be identical to the one used in the experiment conducted at Laboratorie de Mecanique de Lille (LML) (Marquillie et al., 2008). The second case corresponds to the geometry which reproduces the real geometry of the turbomachinery test section of the Czestochowa University of Technology. The test section was created in such a way as to produce the pressure gradient which would correspond to the conditions present in the axial compressor blade channel. The shape of both channels produced initially favorable (FPG) and then adverse pressure gradients (APG), and in this way created conditions for boundary layer separation. Due to a reverse flow where the turbulence transport is dictated by the dynamics of the large-scale eddies such a case is well suited to demonstrate predictive features of the LES technique.

10

Numerical study of flow in a rotor-stator system with inward throughflow

Farzaneh-Gord M., Vazifedoost A., Khoshnevis A. B.

Archives of Mechanics

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2010

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Vol. 62, nr 3

195-214

EN

A numerical study has been carried out to study fluid flow within a rotor-stator system with an inward throughflow and pre-rotation. Furthermore, the effect of flow parameters on the flow structure has been investigated. The entrainment coefficient, beta, of the rotating fluid and the rotating disc moment coefficient have been calculated. A correlation has been found for predicting the place of stagnation point. The results show the Batchelor type of flow with two separated boundary layers on the rotating and stationary discs. The numerical results are compared with the available measured data and generally, a good agreement has been encountered.

11

On Persen theory of two dimensional turbulent boundary layer

Mazumdar H. P., Mandal B. C.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 4

1009-1028

EN

The paper is devoted to the examination of Persen's theory of two dimensional turbulent boundary layers over a smooth flat plate in the light of recent measurements by Österlund. In Persen's approach, the zero-pressure gradient turbulent boundary layer may be divided into two regions only, e.g., I) the inner region, wherein an universally valid structure prevails and modified Spalding's formula is applicable and II) the outer region, which can be described within a similarity framework by a wake law due to Persen. It is shown that the establishment of the theory depends on an experimentally supported relation between the non-dimensional velocity at the end point of the boundary layer and the corresponding non-dimensional distance from the wall. The solution to the problem is achieved by another relation between this velocity and the momentum thickness Reynolds number. The coefficients of skin-friction and velocity profiles, as obtained here for a range of high Reynolds numbers, are found to be in good agreement with Österlund's data. Finally, the results are discussed in the light of the applicability of Österlund's experimental data to the verification of Persen's turbulent boundary layer theory.

12

The structure of turbulent boundary layer with adverse pressure gradient corresponding to turbomachinery condition

Materny M, Dróżdż A, Drobniak S, Elsner W

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2008

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nr 133

221--228

EN

The paper deals with the experimental analysis of turbulent boundary layer at the flat plate for large value of Reynolds number equal Reθ ≈ 3000. The adverse pressure gradient generated by curvature of the upper wall corresponded to the case of pressure variation in axial compressor. The fully developed turbulence structure was achieved by proper triggering of the boundary layer. The mean and turbulent flow – fields were investigated with the use of hot–wire technique.

13

Application of oil – fringe interferometry for measurements of wall shear stress in turbulent boundary layer

Dróżdż A, Elsner W, Drobniak S

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2008

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nr 133

103--110

EN

The measurement of skin friction is presently recognized as a critical element of aerodynamic testing. Skin friction is necessary to characterize wall-bounded flows, to provide critical information necessary for computational simulations and to serve as a sensitive quantity for use in flow-control applications. The paper is aimed at presenting a new technique of precise skin friction measurement applied for a flat plate at the adverse pressure gradient corresponding to pressure distribution in the axial compressor.

14

Convective heat transfer in turbulent boundary layers with transpiration

Meinert J.

Archives of Thermodynamics

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2004

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Vol. 25, no. 4

55-66

EN

Reliable cooling of thermally high stressed components in the field of thrust chamber and turbine technology requires the use of more effective cooling techniques compared to the common recuperative cooling. Alternative cooling techniques basing on mass transfer through the wall such as transpiration cooling are available. For thermal design of transpiration cooled components a detailed knowledge with respect especially to the convective heat transfer behavior in the hot gas boundary layer on the porous wall is requested. This paper describes experimental investigations on this problem as well as the modeling of the measuring results by means of empirical correlations for engineering purposes.