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1

Static instability of an inverted plate in channel flow: state-space representation and solution approximation

Li P., Zhang D., Cui J., Yin H., Yang Y.

Archives of Mechanics

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2023

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Vol. 75, nr 6

695--727

EN

Plate-like structures in channel flow are commonly found in engineering. This paper reports a theoretical study on the static aeroelastic instability of an inverted cantilevered plate in an inviscid channel flow through the state space. This study begins with the kernel function of the flow potential determined in the Fourier domain with the help of the mirror image method. Then, the instability equation is derived from the operator theory and transformed in the state space. Finally, with Glauert’s expansion, model functions, and error functions, the instability problem of such a plate has been modeled as a mathematical function approximation problem and solved by the least squares method. The derived instability equation is considered at the continuum level of description, and no approximation appears at the first equation level. The convergence and reliability of the proposed modeling and its solutions approximation are entirely tested, and it can successfully predict the instability boundary, behavior, and the channel effect. Numerical results show that the decreased channel height and asymmetric plate placement in the channel significantly decrease the critical flow velocity. The plate instability modes are close to the plate’s first natural ones and not sensitive to the channel parameters. This conclusion allows further theoretical exploration of a semi-analytical approximation of the instability boundary from the obtained instability equation. The current modeling strategy in a continuum sense may provide a new idea and essential reference for other instability problems.

2

Second law analysis of mhd forced convective nanoliquid flow through a two-dimensional channel

Miri Rached, Abbassi Mohamed A., Ferhi Mokhtar, Djebali Ridha

Acta Mechanica et Automatica

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2022

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Vol. 16, no. 4

417--431

EN

The present study deals with fluid flow, heat transfer and entropy generation in a two-dimensional channel filled with Cu–water nanoliquid and containing a hot block. The nanoliquid flow is driven along the channel by a constant velocity and a cold temperature at the inlet, and the partially heated horizontal walls. The aim of this work is to study the influence of the most important parameters such as nanoparticle volume fraction (0%≤ϕ≤4%), nanoparticle diameter (5 nm≤dp≤55 nm), Reynolds number (50≤Re≤200), Hartmann number (0≤Ha≤90), magnetic field inclination angle (0≤γ≤π) and Brownian motion on the hydrodynamic and thermal characteristics and entropy generation. We used the lattice Boltzmann method (LBM: SRT-BGK model) to solve the continuity, momentum and energy equations. The obtained results show that the maximum value of the average Nusselt number is found for case (3) when the hot block is placed between the two hot walls. The minimum value is calculated for case (2) when the hot block is placed between the two insulated walls. The increase in Reynolds and Hartmann numbers enhances the heat transfer and the total entropy generation. In addition, the nanoparticle diameter increase reduces the heat transfer and the irreversibility, the impact of the magnetic field inclination angle on the heat transfer and the total entropy generation is investigated, and the Brownian motion enhances the heat transfer and the total entropy generation.

3

Numerical simulation of channel flow over a skewed equilateral cavity

Kamel Abanoub G., Haraz Eman H., Hanna Sarwat N.

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 3

29--43

EN

In this paper, an incompressible, two-dimensional (2D), time-dependent, Newtonian, laminar, and internal channel fluid flow over a skewed equilateral cavity is simulated using the finite difference method (FDM) and alternating direction implicit (ADI) technique. Navier-Stokes equations are solved numerically in stream function-vorticity formulation. The goal of tackling this problem depends on its academic significance by studying the difference between lid-driven and shear-driven cavity flows in terms of the formation of Moffatt eddies at the sharp corner, also to obtain the length and intensity ratios of these counter-rotating vortices. The value of velocity components along the centerlines of the skewed cavity was revealed at low and intermediate Reynolds numbers (Re), typically (Re = 200 and 2000) at two different skew angles of mainly 30° and 45°. Likewise, the blocked-off regions’ method is used to deal with the geometry of the skewed cavity especially the sharp corners. Furthermore, as Re increases, the main vortex approaches the skewed cavity center and the counter-rotating vortices get bigger in size and intensity, and their number increases.

4

Numerical simulation of the micropolar fluid flow and heat transfer in a channel with a shrinking and a stationary wall

Ali K., Ashraf M.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 2

557--569

EN

We present the numerical study of hydromagnetic (MHD) flow and heat transfer characte- ristics of a viscous incompressible electrically conducting micropolar fluid in a channel with one wall shrinking and the other at rest in the presence of a transverse applied magnetic field. Different from the classical shooting methodology, we employ a combination of a di- rect and an iterative method (SOR with optimal relaxation parameter) for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar nonlinear ODEs. Effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigation may be beneficial to the flow and thermal control of polymeric processing.

5

Impact of transversely-oriented wall corrugation on hydraulic resistance of a channel flow

Szumbarski J., Blonski S., Kowalewski T. A.

Archive of Mechanical Engineering

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2011

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Vol. LVIII, nr 4

441-466

EN

The impact of the transversely-oriented sinusoidal wall corrugation on the hydraulic drag is investigated numerically for the flow through the channel of finite width and with flat sidewalls. The numerical method, based on the domain transformation and Chebyshev-Galerkin discretization, is used to investigate the flow resistance of the laminar, parallel and pressure-driven flow. The obtained results are compared to the reference case, i.e., to the flow through the channel with rectangular cross section of the same aspect ratio. Simple explanation of the gain in the volumetric flow rate observed in the flow through spanwise-periodic channel with long-wave transversely-oriented wall corrugation is provided. In the further analysis, pressure drop in the flows with larger Reynolds numbers are studied numerically by means of the finite-volume commercial package Fluent. Preliminary experimental results confirm the predicted tendency.

PL

Przedmiotem artykułu jest analiza numeryczna wpływu poprzecznego sinusoidalnego pofalowania ścian na opory hydrauliczne przepływu cieczy lepkiej w kanale. Do wyznaczenia stacjonarnego pola ruchu cieczy lepkiej w kanale posłużono się transformacją obszaru i spektralną metodą Czebyszewa-Galerkina. Obliczone wartości strat ciśnienia porównano z przepływem laminarnym w kanale o ścianach płaskich i przekroju prostokątnym, przy zachowaniu takiej samej wartości stosunku szerokości kanału do jego wysokości. Podano objaśnienie efektu zmiejszenia oporów hydraulicznych w przypadku poprzecznego pofalowania o dużej długości fali. Omówiono również wyniki analizy wpływu pofalowania ścian na straty ciśnienia dla przepływów z większymi liczbami Reynoldsa, uzyskane przy pomocy komercyjnego programu Fluent. Przedstawiono wstępne wyniki badań eksperymentalnych, które potwierdzają zależności otrzymane w modelach numerycznych.

6

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.

7

Unsteady two-fluid flow and heat transfer of conducting fluids in channels under transverse magnetic field

Linga Raju T., Sreedhar S.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 4

1093-1114

EN

An attempt has been made to investigate the behaviour of flow formation and heat transfer aspects on an unsteady MHD two-fluid flow of electrically conducting fluids under the influence of a transversely applied uniform magnetic field in a horizontal channel. The flow is driven by a constant uniform pressure gradient in a channel bounded by two parallel walls, one being stationary and the other oscillating. The two fluids are assumed to be incompressible and electrically conducting possessing different viscosities, thermal and electrical conductivities. The transport properties of the two fluids are taken to be constant and the bounding walls are maintained at constant and equal temperature. The governing partial differential equations are reduced to the ordinary linear differential equations using two-term series, and which in turn are solved analytically to obtain exact solutions for the velocity distributions and the corresponding temperature distributions in the two-fluid regions respectively. Profiles of these solutions are plotted to illustrate the details of the flow and heat transfer characteristics and their dependence on some of the physical parameters, such as the Hartmann number, ratios of the viscosities, heights, electrical and thermal conductivities. And, it is shown how the velocity and temperature distributions vary with hydromagnetic interaction in the case of steady flow and unsteady flow motions. Also, as expected, it is observed that these distributions are pronounced more in the unsteady state when compared to the steady state problem.

8

Turbulent kinetic energy budget in a gravel-bed channel flow

Mignot E., Barthélemy E., Hurther D.

Acta Geophysica

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2008

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Vol. 56, no. 3

601-613

EN

The present experimental investigation focuses on the characteristics of near bed turbulence in a fully rough, uniform open-channel flow over a gravel-type bed. Due to bed topography small scale heterogeneity, the flow is not uniform locally in the near bed region and a double averaging methodology is applied over a length scale much larger than the gravel size. The double-averaged Turbulent Kinetic Energy (TKE) budget derived in the context of the present flow over a gravel bed differs from the TKE budget written for flow over a vegetation canopy. The non-constant shape of the roughness function measured in our gravel bed leads to an additional bed-induced production term which is null for vertical roughness elements, such as simplified vegetation elements. The experimental estimation of the terms of the TKE budget reveals that the maximum turbulent activity takes place away from the reference plane, near the roughness crests. However, within the interface sublayer the work of the bed induced velocity fluctuations against the Reynolds stress is of the same magnitude as the main turbulence production term. Consequently, the characteristics of the TKE budget have similarities with uniform flows over canopies and strongly differ from uniform flows over smooth and transitionally rough flows over sedimentlike beds.

9

Exact solutions for incompressible couette flow with constant temperature and constant heat flux on walls in the presence of radiation

Chaudhary R. C., Jain P.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 4

929-939

EN

The present paper investigates a closed form solution for the transient free convection flow of a viscous incompressible fluid between two infinite vertical paranel plates in the presence of radiation. The flow is set up due to free convective currents occurring as a result of application of a constant heat flux (CHF) at one wall and a constant temperature on the other wall. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The goveming coupled non-linear partial differential equations have been solved exactly using the Laplace-transform technique. The numerical values obtained from analytical expressions of velocity, temperature, skin-mction and the Nusselt number have been presented graphically to study the behaviour of flow on the momentum and thermal boundary layer.

10

Efficient implementation of a compact-pseudospectral method for turbulence modeling

Tyliszczak A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2006

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Vol. 10, No 2

125-138

EN

The paper is devoted to parallel implementation of a compact discretization scheme com-bined with the Fourier pseudospectral method. The idle time of processors resulting from the method of computating derivatives using compact schemes is eliminated by proper ordering of subtasks and by performing useful computations when processors are waiting for data from their neighbors. The correctnes of the algorithm is confirmed by comparison of results of LES simulations with DNS data for flow in a 3D channel with periodic non-slip wall boundary conditions.

11

Oscillatory hartmann two-fluid flow and heat transfer in a horizontal channel

Umavathi J. C., Mateen A., Chamkha A. J., Al-Mudhaf A.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 1

155-178

EN

An unsteady Hartmann flow of two immiscible fluids through a horizontal channel with time-dependent oscillatory wall transpiration velocity is investigated. One of the fluids is assumed to be electrically conducting while the other fluid and the channel walls are assumed to be electrically insulating. Separate solutions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The partial differential equations governing the flow and heat transfer are transformed to ordinary differential equations and closed-form solutions are obtained in both fluids' regions of the channel for steady and unsteady conditions. The closed-form results are presented graphically for various values of the Hartmann number, frequency parameter, periodic frequency parameter viscosity and conductivity ratios as well as the Prandtl number to show their effect on the flow and heat transfer characteristics.

12

Selected Possibilities to Improve Pumps and Pump Systems

Jędral W., Błaszczyk A.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2005

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nr 128, vol. 1

265-272

EN

Some contemporary problems concerning the pump efficiency, reliability and life span, diagnostics, as well as the question of their proper selection procedure and of their control systems are presented in the paper. These problems are illustrated with selected results of the author's own studies. Limiting barriers to perform advanced research work in domestic technical universities are pointed out.

13

Linear stability of two-dimensional flow to three-dimensional perturbations in a channel with a flexible wall

Sibanda P., Motsa S. S., Shateyi S.

Archives of Mechanics

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2004

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Vol. 56, nr 4

293-311

EN

In this paper we investigate the effects of three-dimensional disturbance waves on the stability of a two-dimensional channel flow with one compliant surface. The study exploits the multideck structure of the flow in the limit of large Reynolds numbers to make an asymptotic analysis of the flow and to derive linear neutral stability results. The study shows that for a flow over flexible surfaces, three-dimensional disturbances may be more unstable than two-dimensional modes for a given set of wall properties.

14

Magnetohydrodynamic fully developed combined convection flow between vertical plates heated asymmetrically

Ghosh S., Nandi D.

Journal of Technical Physics

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2000

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Vol. 41, no 2

173-185

EN

Magnetohydrodynamic (MHD) fully developed flow of a viscous incompressible electrically conducting fluid in a vertical channel during combined convection, with asymmetric heating of the wall, under the influence of a constant pressure gradient and in the presence of an uniform transverse magnetic field, is studied. Exact solution of the governing equation is obtained in a closed form. The solution in dimensionless form contains two pertinent flow parameters, viz. M (the Hartmann number) and Gr(the Grashof number). The limiting cases of a MHD forced and free convection are analyses, what has not beem done earlier in the literature. The occurrence of flow reversal indicates that there arises a flow reversal at the cold wall when r[sub T] = 1 while, for r[sub T] < 1, no flow reversal is possible in the absence of magnetic forces.

15

Magnetohydrodynamic convective flow in a rotating channel

Ghosh S., Bhattacharjee P.

Archives of Mechanics

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2000

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Vol. 52, nr 2

303-318

EN

Combined free and forced convective flow of an electrically conducting viscous incompressible fluid in a rotating parallel plate channel with perfectly conducting walls is investigated. Exact solutions of the governing equations for the fully developed flow are obtained in closed form. It is found that the resultant shear stresses at the walls decrease with the increase in both the rotation parameter K^2 and the magnetic parameter M^2. The rate of heat transfer at both walls decreases with the increase in the Grashof number G.

16

Weight vector in designing of primary transducers for electromagnetic flow meters

Michalski A., Wincenciak S.

Archives of Electrical Engineering

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1998

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Vol. 47, nr 1

81-99

EN

The design of primary transducer for electromagnetic flow meter uses the distribution of weight function as a starting point to determining the required distribution of exciting magnetic field. Two basic methods of the weight function determination for restricted group of flow channels are presented in the paper. Based on existing methods, authors present a new approach to the calculation of weight function distribution for a very wide group of flow channels. Paper presents a design algorithm for rectangular and trapezoidal flow channels with varying bed-to-water conductivity ratio with some remarks concerning to the optimization of metrological properties of flow meter.

PL

W procesie projektowania przetwornika pierwotnego przepływomierza elektromagnetycznego wykorzystuje się rozkład funkcji wagi jako punkt wyjścia do określania żądanego rozkładu wzbudzanego pola magnetycznego. W artykule przedstawiono dwie, dotychczas stosowane, podstawowe metody wyznaczania rozkładu funkcji wagi dla ograniczonej klasy przepływomierzy. Na bazie istniejących metod zaproponowano uogólnioną metodę wyznaczania rozkładu funkcji wagi dla szerokiej gamy kanałów przepływowych. Przedstawiono metodykę projektowania kształtu cewki przetwornika pierwotnego wykorzystującą zaproponowaną metodę, uzupełnioną o przykładowe wyniki obliczeń optymalizacyjnych dla wybranej grupy kanałów przepływowych.