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otrzymywanymi z powszechnie rekomendowanego równania Colebrooka-White’a. Następnie za pomocą wskaźników w postaci błędu średniego, błędu względnego i maksymalnego błędu względnego została przeprowadzona analiza porównawcza. Równanie Colebrooka-White’a nie da się przekształcić do postaci jawnej, dlatego wymaga ono rozwiązania iteracyjnego. Zbieżność współczynnika oporów liniowych na poziomie mniejszym niż 0.1 % wymaga zwykle co najmniej 6 przybliżeń. Ostatecznie udało się stwierdzić, że wiele dostępnych przybliżeń równania Colebrooka-White’a jest bardzo dokładna.
recommended Colebrook-White equation. Subsequently, a comparative analysis was conducted using indicators such as mean error, relative error, and maximum relative error. The Colebrook-White equation cannot be transformed into explicit form, requiring an iterative solution. Convergence of the linear resistance coefficient at a level lower than 0.1% typically requires at least 6 approximations. Ultimately, it was found that many available approximations of the Colebrook-White equation are highly accurate.
(0.00–0.05), the diameter of the NPs (30–100 mn) and the orientation of square cylinder (0–90). The numerical results were expressed in terms of isotherm contours and average Nusselt number to explain the effect of relevant parameters. Over the range of conditions, the separation of the boundary layers of nanofluids increased with the size of the NPs as compared to pure water. NPs volume fraction and its size had a significant effect on heat transfer rate. The square cylinder of orientation angle (45) gained a more efficient heat transfer cylinder than other orientation angles. Finally, the correlations were developed for the average Nusselt number in terms of the relevant parameters for 45 orientation of the cylinder for new applications.
using the Runge-Kutta method. The perturbations of these basic solutions are expressed in the form of three-dimensional Tollmien-Schlichting waves. The formulation of the stability problem leads to the Orr-Sommerfeld equation modified by the permeability parameter (Darcy number) and the small Reynolds number. This equation is given in a general form which can be applied to the Chebyshev domain and the boundary layer domain and solved numerically using the Chebyshev spectral collocation method. The marginal stability diagrams, the critical Reynolds numbers and the eigenvalue spectra are obtained for different values of the parameters which have modified the stability equation. Numerical solutions indicate the importance of the effect of these parameters on the flow stability characteristics.
ciekłej stali przepływającej przez dwuwylewową kadź pośrednią. Głównym parametrem, na który zwrócono uwagę w badaniach była prędkość przepływu ciekłej stali kształtująca się w przestrzeni roboczej wylewu osłonowego oraz w objętości kadzi pośredniej. Określono również wpływ turbulencji na procentowy objętościowy udział poszczególnych przepływów oraz na stopień mieszania kąpieli metalowej.
steel hydrodynamics flowing through the two-strand tundish. The main parameter noted in the article was velocities in the working space of ladle shroud and in the volume of the tundish. The influence of the turbulence on the percentage volume of the individual flows and the mixing degree of the metal bath was also determined.
plaques formation. Methods: To study the mechanically regulated plaque formation, the flow fields in artery blood vessels with different stenosis rates at various Reynolds numbers were simulated numerically with the two-dimensional axisymmetric models, and the hemodynamic characteristics around the plaque were scaled with stenosis rate and Reynolds number. Results: The results showed that increases of both Reynolds number and stenosis rate facilitated the occurrence of flow separation phenomenon, extended recirculation zone, and upregulated the maximum normalized wall shear stress near the plaque throat section while downregulated the minimal normalized wall shear stress at the front shoulder of plaque, as it should be; in the atherosclerotic plaque leeside of the recirculation zone, an obvious catch bond region of wall shear stress might exist especially under low Reynolds number with stenosis rate smaller than 30%. This catch bond region in the plaque leeside might be responsible for the LBF (low blood flow)-enhanced formation of the atherosclerotic plaque. Conclusions: This work may provide a novel insight into understanding the biomechanical effects behind the formation and damage of atherosclerotic plaques and propose a new strategy for preventing atherosclerotic diseases.
Praktyczna część pracy polegała na zbudowaniu stanowiska pomiarowego, umożliwiającego wyznaczenie parametrów przepływu wody w rurociągu zgodnie z aktualnie stosowanymi w przemyśle metodami i przyrządami pomiarowymi. Przeprowadzono szereg pomiarów i obliczeń, a następnie dokonano analizy uzyskanych wyników i sformułowano wnioski.
aim of the practical part of thesis was to build a measuring position enabling the determination of water parameters in the pipeline in accordance with measurement methods and instruments currently used in industry. A number of measurements and calculations were carried out, and then the results obtained were analyzed and conclusions were formulated.
przede wszystkim dla przypadku, kiedy mieszadło pompowało ciecz na dół zbiornika. Dla mieszadeł o łopatkach usytuowanych prostopadle do płaszczyzny mieszadła wzrost mocy nie występował.
relative increase in power consumption. For impellers with blades located perpendicular to the agitating plane, this phenomenon did not occur.
75°C. Design of each plate provided with eleven thermocouple sensors to determine the temperatures, in which seven were used to measure the surface temperature of plate and four were used to measure the inlet and outlet bulk temperature of cold and hot fluids. The mass flow rate of test fluid, varied between 0.5 to 4 liters per minute and corresponding steady state temperatures is measured. Using experimental readings, temperature difference between the inlet and outlet streams (∆T), logarithmic mean temperature difference (LMTD) and overall heat transfer coefficient (U) are determined. The obtained ∆T and U values of corrugation angles (30°, 50°) of CPHE were compared with those of flat plate heat exchangers. For corrugation angle of 30° and 50°, the ∆T and U values increases with increase of mass flow rate of the fluid. The turbulence in the flow increases due to increase in the corrugation angle, which results in the enhancement of heat transfer. Moreover, thermal effectiveness (ε) is estimated using NTU method and compared for all the plates. As the NRe values gradually increases, ε decreases for flat plate and CPHE (θ = 30° and θ= 50°). At low NRe value of 114, observed a maximum ε (≅0.998) value for corrugated angle of 50°. There is adequate contact time between the cold and hot fluids at low Reynolds number, so maximum rate of heat transfer is possible, as a result ε values are high.
the cavity move with a uniform velocity. The flow variables are simulated below the critical Reynolds numbers with isothermal and mass-transfer conditions in the square cavity. We have used a streamfunction-vorticity (ψ - ξ) formulation to investigate the fluid flow in terms of flow variables ψ, ξ, T and C at low Reynolds numbers (Re). The Prandtl number (Pr) and Schmidt number (Sc) have been chosen as 6:62 and 10, 50, 100, 150 respectively, in order to calculate the numerical solutions of T and C. The matrix method has been used to evaluate the stability and convergence of the numerical scheme. The conditions obtained from the matrix method have been used to arrive at the numerical solutions with desired accuracy.
for convective fluxes upwind and central differencing schemes are blended using a ‘deferred correction’ approach. A simplified pressure correction equation is derived, and proper under-relaxation factors are used so that computational cost is reduced without adversely affecting the convergence rate. The governing equations are expressed in Cartesian velocity components and solution is carried out using the SIMPLE algorithm for collocated arrangement of variables. The mesh yielding grid-independent solution is then utilized to study, for the very first time, the effect of the Reynolds number on the separation bubble length, separation angle, and drag coefficients for both circular and square cylinders. Finally, functional relationships between the computed quantities and Reynolds number (Re) are proposed up to Re = 40. It is found that circular cylinder separation commences between Re= 6.5-6.6, and the bubble length, separation angle, total drag vary as Re, Re-0.5, Re-0.5 respectively. Extrapolated results obtained from the empirical relations for the circular cylinder show an excellent agreement with established data from the literature. For a square cylinder, the bubble length and total drag are found to vary as Re and Re-0.666, and are greater than these for a circular cylinder at a given Reynolds number. The numerical results substantiate that a square shaped cylinder is more bluff than a circular one.
results for velocity and pressure in horizontal and vertical directions through the centre of a rectangular region are elucidated. The nature of velocity profiles and pressure for different Reynolds numbers in the horizontal and vertical directions through the geometric centre was analyzed with the help of pictorial representations. The present results are compared with the available benchmark results and we have found that they are not in disagreement.
the coefficient of friction of gas transportation in the pipeline at intervals of the absolute pressure from 220 to 2 kPa and M < 1 Mach numbers, depending on the diameter and length of the pipeline and physical and technological characteristics of the gas. The K1* aspect ratio is proposed, which characterizes in time the ratio of the dynamic force of movement of gas to the static pressure related to the diameter of the pipeline. The coefficient of air friction was modeled according to the vacuum pressure as a parameter of density and air flow. Air flow was taken from 1.917·10-3 m 3/s to 44.5·10-3 m 3/s respectively, diameters from 0.030 to 0.070 m and Mach number was M = 0.005-0.13. At the vacuum and excess pressures with increasing of Reynolds number and decreasing of Mach number the gas friction coefficient increased linearly. According to the simulation results as the pressure loss and the diameter of the pipeline are increased the friction coefficient increased as well. Analogically, at the vacuum metric pressure when the pressure loss and the diameter of the pipeline are increased the friction coefficient increased. At the pipeline internal diameters of 22, 30, 36 mm accordingly for pressure losses from 2 to 14 kPa the coefficient of air friction varies from 0.006 to 54.527 respectively.
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addition, a MATLAB code was developed and validated by comparing the results with the reference values from literature. Staggered grid was employed in the discretization of the cavity to avoid checkerboard pressure while developing the code. The governing equations were discretized in terms of velocity and pressure fields. The artificial compressibility method was used to de-couple the pressure and velocity terms in the governing equations. A 129×129 grid system was used in both cases. The effects of Reynolds number (100≤ Re ≤ 1000) on the flow characteristics were illustrated through an analysis of stream function, velocity vector, pressure co-efficient and velocity contours. The thinning of the wall boundary layers with an increase in the Reynolds number is evident from the u and v velocity profiles along the vertical and horizontal lines at the geometric center, although the rate of this thinning is very slow for Re> 5000.
blocks of combustion engines. Physics and conditions influencing processes on liquid – washed operational surface phase boundary have been justified. Out of the contemporary hypotheses explaining the physics of cavitation erosion, the bubble theory has been considered. A mathematical model of erosion has been presented in the context of cavitation implosion energy determining crash interactions of liquid cumulative fluxes on the washed surface. Occurring plastic deformations have been graphically explained linking them with the occurrence of fatigue micro-cracks and later with erosive pits. Influence of initial steel hardness on intensity of cavitation erosion has been checked. Discussion of ways to increase metal surface resistance to cavitation erosion has been carried out.
has been implemented to discretize the governing equations of the present problem. The well known SIMPLE algorithm is employed for pressure-velocity coupling. This was executed with the aid of a computer program developed and run in a C-compiler. Computations have been performed for unknown variables with Reynolds numbers (Re) = 50, 100, 250, 500, 750 and 1000. The behavior of steady-state solutions of velocity and pressure of the fluid along horizontal and vertical through geometric center of the rectangular domain have been illustrated. We observed that, with the increase of the Reynolds number, the absolute value of velocity components decreases whereas the pressure value increases.
efekcie może prowadzić do zaburzeń strumienia przepływu. Wiarygodność pomiaru tego parametru, mogą zapewnić kryzy segmentowe. W artykule zaprezentowano wyniki badań przepływowych kryz segmentowych z przytarczowym punktowym odbiorem ciśnienia różnicowego, przy niewielkich liczbach Reynoldsa oraz symulacje numeryczne dla wybranej kryzy. W badaniach jako medium wykorzystano wodę.
installation. However, there is a need for using cheap but reliable systems to measure the flow of the injected fuel. In real operating conditions various residues may often deposit in fuel transmission systems, which in turn can lead to flow fluctuations. Reliable flow factor measurement requirements can be met by segmental orifices. In the article, based on a research and measurement station, presented were the results of flow measurements with segmental orifices with point reception of differential pressure for small Reynolds numbers as well as numerical simulations. For the selected segmental orifice the flow factor characteristic in the function of the Reynolds number was calculated. In the research, water was used as the medium; the next stage of the research will involve the realization of the proposed solution with the use of hydraulic oil.
Liquid), jako paliwa w energetyce ciepłowniczej. Pozwala to na obniżenie zawartości NOx i SOx bez konieczności inwestowania w drogie układy odsiarczania i odpylania, co jest atutem ekologicznym i ekonomicznym. Wymagane, ze względów technologicznych, układy pomiaru strumienia dostarczanego paliwa, powinny być tanie w eksploatacji, niezawodne oraz odporne na zanieczyszczenia. Warunki te mogą spełnić kryzy mimośrodowe lub segmentowe. W artykule przedstawiono stanowisko doświadczalno-pomiarowe, pozwalające na przeprowadzenie przepływowych badań wstępnych, kryz mimośrodowych z punktowym odbiorem ciśnienia różnicowego, przy małych liczbach Reynoldsa. Wyniki wykonanych pomiarów charakterystyk przepływowych oraz symulacji numerycznych przedstawiono w tabelach i na wykresach. Dla wybranej kryzy mimośrodowej wyznaczono wartość współczynnika przepływu C w funkcji liczby Reynoldsa. Przedstawione w artykule analizy dotyczą przepływu wody. Planowane są dalsze badania dla oleju hydraulicznego.
using coal and water-based CWL (Coal-Water Liquid) suspensoids as fuel in the heating industry. Using this fuel leads to a reduction in NOx and SOx percentage without the need for an expensive desulphurization and dust extraction installation, which is a huge economic and ecological advantage. For technological reasons required are systems for measuring the flow of the injected fuel that are cheap in use, reliable and residue-resistant. These requirements can be met by segmental and eccentric orifices. In the article, presented was a research and measurement station which enables its users to conduct introductory flow measurements for eccentric orifices with point reception of differential pressure for small Reynolds numbers. The results of the flow characteristic measurements as well as of numerical simulations were presented in the form of tables and charts. For the selected eccentric orifice the C flow parameter in the Reynolds number function was determined. The analysis of the study results presented in the article refers to the flow of water. The next planned stage of the research will involve flow studies and measurements with the use of hydraulic oil as the medium.
turbulent single phase flows through circular 90˚ curved bend for different curvature ratio (Rc/D = 1 to 5), defined as the bend mean curvature radius (Rc) to pipe diameter (D) is investigated numerically for different Reynolds number (Re) ranging from 1×105 to 10×105. The purpose of this study is to simulate numerically the flow pattern and characterize the swirling secondary flow in 90˚ bends. Flow simulation using CFD techniques are performed to understand these phenomena. The k − " model with SIMPLE method is used for present study. After validation of present model with published experimental data, a detail study has been performed to characterize the flow separation and the dependency of swirl intensity on Reynolds number and curvature ratio in 90˚ pipe bend for single phase turbulent flow.
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prowadzonych w kolumnie z upakowanym złożem, zawierającym rudę i dodatki. Ustalony został wpływ różnych dodatków (piryt, siarka, szkło i polietylen) na stopień odzysku miedzi z rudy łupkowej. Do badań zostały użyte bakterie Acidithiobacillus ferrooxidans, pochodzące z własnej kolekcji. Bakterie były hodowane na dwóch pożywkach – 2K i 9K. Surowcem użytym w badaniach był odpad z pierwszego czyszczenia, pochodzący z Zakładu Wzbogacania Rud Lubin. Materiał ten zawierał najwięcej minerałów wchodzących w skład rudy łupkowej. Doświadczenia przeprowadzono, stosując różne ilości dodatków do złoża rudy, znajdującej się w kolumnie. Badania wskazały na istotną rolę, jaką odgrywa immobilizacja (unieruchomienie) komórek bakteryjnych na powierzchni ciał stałych w procesie bioługowania. Określony został wpływ warunków hydrodynamicznych istniejących w porowatym złożu na odzysk miedzi. W optymalnych warunkach odzysk miedzi przekroczył 70% po 14 dniach prowadzenia procesu bioługowania.
(pyrite, sulphur, glass, and polyethylene) to the black ore on the copper recovery during the black shale bioleaching has been evaluated. For the bacteria growth two different media (2K and 9K) were used. The ore material selected for the bioleaching experiments was taken from the industrial flotation circuit (middlings from 1st cleaning) from Lubin Concentrator. The bioleaching tests were conducted with different amounts of additives which were added to the column packed with black shale ore. These experiments reveal that the microbial cells immobilization has an effect on the copper recovery. The role of hydrodynamic conditions in porous media is also described in the context of copper recovery. Under the optimal conditions, the extraction of copper was obtained more than 70% in 14 days, which is better than bioleaching without additives.
rezonansowej generatora H = 20, 40, 60 mm. Dokonano pomiaru mocy elektrycznej przetwornika elektroakustycznego. Porównano uzyskane wartości liczb Reynoldsa oraz Stokesa z danymi literaturowymi oraz warunkiem powstawania strugi syntetycznej, uzyskując zbieżność otrzymanych wyników.
mm. Electrical power of electroacoustic transducers was measured. Obtained values of Reynolds and Stokes numbers were compared with literature data, and the criterion for synthetic jet formation. Convergence of the obtained results was gained.
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