Analysis of the Subsonic and Supersonic Flow Using Analytical and Numerical Methods

2015 ◽  
Vol 816 ◽  
pp. 16-26
Author(s):  
Mária Čarnogurská ◽  
Tomáš Brestovič ◽  
Miroslav Příhoda ◽  
Marián Lázár ◽  
Natália Jasminská
Keyword(s):  
Numerical Methods ◽  
Cross Section ◽  
Subsonic Flow ◽  
Flow Conditions ◽  
Relative Duration ◽  
Tunnel Length ◽  
Dimensionless Velocity ◽  
Proportional Value ◽  
Flow Through ◽  
Flow Cross

The article presents the analysis of the 1D flow of compressible fluid by means of analytical and numerical methods. The results from the solution showed that the calculation of dimensionless velocity for particular flow conditions varies in the area of subsonic flow only a very little, when using both methods. It was found that the dependence of dimensionless velocity on the relative duration of the investigated tunnel applies universally. For any proportional value of the tunnel length x/L and the constant ratio of outlet and inlet cross section of the tunnel level equal to 0.6474, the course of the dimensionless velocity for each tunnel, which satisfies the above condition, will always be the same. This means that also the nature of flow in any such tunnel will exhibit the same properties. This finding provides new knowledge from the analysis of air flow through a channel with a variable flow cross section.

Analytical Solution for Newtonian Laminar Flow Through the Concave and Convex Ducts

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
M. Firouzi ◽  
S. H. Hashemabadi
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Friction Factor ◽  
Cross Section ◽  
Cross Sections ◽  
Fully Developed Flow ◽  
Pipe Flows ◽  
Dimensionless Velocity ◽  
Flow Through ◽  
Fanning Friction Factor

In this paper, the motion equation for steady state, laminar, fully developed flow of Newtonian fluid through the concave and convex ducts has been solved both numerically and analytically. These cross sections can be formed due to the sedimentation of heavy components such as sand, wax, debris, and corrosion products in pipe flows. The influence of duct cross section on dimensionless velocity profile, dimensionless pressure drop, and friction factor has been reported. Finally based on the analytical solutions three new correlations have been proposed for the product of Reynolds number and Fanning friction factor (Cf Re) for these geometries.

Velocity field and discharge measurements at the turbine inlet of Iron Gate 2 hydropower plant

2021 ◽  
Author(s):  
Damjan Ivetic ◽  
Dusan Prodanovic ◽  
Predrag Vojt
Keyword(s):  
Physical Model ◽  
Cross Section ◽  
Flow Measurement ◽  
Steel Frame ◽  
Control Flow ◽  
Flow Conditions ◽  
Discharge Measurement ◽  
Flow Cross Section ◽  
Iron Gate ◽  
Flow Cross

<p>To define the performance characteristics of turbines in Hydropower Plants (HPP) accurate hydraulic, mechanical and electrical quantities are needed. The discharge is the most difficult quantity to measure and assess its uncertainty (Adamkowski, 2012). Traditionally, during field acceptance tests the discharge is measured using velocity-area method. Often, no direct flow measurements are possible and only index methods are used, with flow coefficients obtained during physical model testing. In the non-standard situations, with adverse flow conditions this may lead to unpredicted flow uncertainty.</p><p>             The system used at the Iron Gate 2 HPP for control flow measurement at the inlet of bulb turbine is presented in this paper. The HPP is situated on a Danube river, between Serbia and Romania and is operational from 1985. The HPP is equipped with 20 horizontal Kaplan low head bulb turbines. The physical model experiments (JČInstitute, 2006) have concluded that due to the upstream flow conditions, the incident water flow direction is not parallel to the turbines (depending on operating conditions and can be up to 40<sup>o</sup>) as was assumed during the turbine’s model tests, raising the question of used Winter-Kennedy’s method accuracy.</p><p>             To perform a control flow measurement, a modular velocity-area system was designed. The system can be installed at the intake of any turbine, upstream of the trash rack. It consists of the 14.5x3.1 m steel frame, shaped to minimize flow disturbances, which can be traversed vertically through the flow cross section (28 m). Due to the high incident angles and large vortices in the front of the trash rack, propeller current meters were not suitable. The novel spherical 3D electromagnetic velocity meter (EMVM) was developed (Svet Instrumenata), enabling fast and continuous measurements of all the velocity vector components, with low flow disturbance. The 15 EMVMs were mounted on the frame and connected into the measurement network. Redundant velocity measurement was done using 2 Nortek “Vector” ADVs (Nortek). The measurement network also comprises of 2 water level pressure transducers and 2 steel frame position transducers (UniMeasure). All measurements were synchronized with HPP’s SCADA, so turbine’s operational parameters were downloaded off-line and merged.</p><p>             During the 2020, measurement system was used on the two turbines. The velocity profile was measured using two strategies: incrementally, the steel frame was raised from the bottom (average depth of 26 m) in increments of ~1.0 m and kept for at least 10 min in fixed position, and continuous where the steel frame was traversed through the flow cross-section with a constant speed of 0.05 m/s. Uncertainty assessment procedure, specifically tailored for this application, yielded discharge measurement uncertainties between 1.02 % and 2.00 %  for incremental, and between 1.65 % to 2.79 % for continuous regime.</p><p>References</p><p>Adamkowski, A. (2012). Discharge measurement techniques in hydropower systems with emphasis on the pressure-time method. Hydropower-practice and application.</p><p>Jaroslav Černi Institute (2006). Scale model investigation of turbine runner inflow at an unfavorable angle at HPP „Đerdap II“, SDHI (in Serbian)</p><p>NORTEK: https://www.nortekgroup.com/products/vector-300-m</p><p>Svet Instrumenata: http://www.si.co.rs/index-e.html</p><p>UniMeasure: https://unimeasure.com/wp-content/uploads/2019/12/HX-EP-SERIES-CATALOG-PAGES-1.pdf</p>

The Stability of Flow Through Porous Screens

1960 ◽  
Vol 64 (594) ◽  
pp. 359-362 ◽  
Author(s):  
P. G. Morgan
Keyword(s):  
Pressure Drop ◽  
Sufficient Information ◽  
Flow Conditions ◽  
Flow Through ◽  
The Stability

In many cases of the flow through porous screens, one may consider it to be made up of a number of jets passing through the openings of the screen. These jets are separated by a series of wakes behind the solid parts of the screen. The majority of investigations on the flow through such screens have been concerned with the measurement of pressure drop and its variation with different flow conditions; it has been assumed that the pressure is discontinuous at the screen itself and that the pressure drop coefficient Δp/½ρυ2 provides sufficient information, where Δp is the pressure drop across the screen, ρ the density of the fluid, and υ the velocity of approach to the screen.

Modeling of the Ionized Fluid Flow through a Cone-Shaped Nanopore

2007 ◽  
Vol 121-123 ◽  
pp. 1089-1092 ◽  
Author(s):  
Jian Zhong Fu ◽  
Xiao Bing Mi ◽  
Yong He ◽  
Zi Chen Chen
Keyword(s):  
Fluid Flow ◽  
Theoretical Analysis ◽  
Cross Section ◽  
Debye Length ◽  
Velocity Profiles ◽  
Gradual Change ◽  
Ion Flow ◽  
Flow Through

Theoretical analysis of the ionized fluid flowing through a cone-shaped nanopore is presented. The internal cross section of the cone-shaped channel is in the range from micro- to nanometer and gradual change from larger to smaller than the Debye length for the ions. The model is developed to predict the ionized fluid flow behaviors in cone-shaped micro/nanochannels. The velocity profiles of ion flow that occur in nanopores are obtained.

Prediction of Fluid Flow in Artificial Cancellous Bone

2014 ◽  
Vol 695 ◽  
pp. 393-397
Author(s):  
Elsa Syuhada Abdull Yamin ◽  
Nor Azwadi Che Sidik
Keyword(s):  
Fluid Flow ◽  
Pore Size ◽  
Surface Area ◽  
Pore Diameter ◽  
Bone Surface ◽  
Flow Conditions ◽  
Morphological Aspects ◽  
Flow Through ◽  
Structure Result ◽  
Dynamics Method

The permeability of the blood in the artificial cancellous are affected by certain morphological aspects that include pore diameter, pore size, porosity and the bone surface area. In this study, computational fluid dynamics method is used to study the fluid flow through the cancellous structure. Result of the present work show that geometries with the same porosity and overall volume can have different permeability due to the differences in bone surface area. The hexahedron geometry has the highest permeability under stimulated blood flow conditions, where the cylindrical geometry has the lowest. Linear relationship is found between permeability and the two physical properties, bone surface area and the pore size.

High Speed Flow through Perforated Plates

1960 ◽  
Vol 64 (590) ◽  
pp. 103-105
Author(s):  
P. G. Morgan
Keyword(s):  
Pressure Drop ◽  
High Speed ◽  
Perforated Plate ◽  
Wire Mesh ◽  
Flow Conditions ◽  
High Speed Flow ◽  
Perforated Plates ◽  
Speed Flow ◽  
Flow Through ◽  
Points Of View

The flow through porous screens has been widely studied from both the theoretical and experimental points of view. The most widely used types of screen are the wire mesh and the perforated plate, and the majority of the literature has been concerned with the former. Several attempts have been made to correlate the parameters governing the flow through such screens, i.e. the pressure drop, the flow conditions and the geometry of the mesh.

Correlation Between LDA and Ultrasound Heart Catheter Measurements in a Stenosed Arterial Model

1995 ◽  
Vol 117 (1) ◽  
pp. 103-106 ◽  
Author(s):  
D. Liepsch ◽  
A. Poll ◽  
R. Blasini
Keyword(s):  
Cross Section ◽  
Laser Doppler Anemometry ◽  
Water Solution ◽  
Maximum Velocity ◽  
Symmetric Model ◽  
Axially Symmetric ◽  
Flow Conditions ◽  
Future Studies ◽  
Glycerine Water ◽  
Arterial Model

Ultrasound heart catheters are used to measure the velocity in coronary arteries. However, the act of introducing a catheter into the vessel disturbs the very flow being measured. We used laser Doppler anemometry to measure the velocity distribution in an axially symmetric model, both with and without a catheter inserted. The catheter reduced the center-line velocity by as much as 60 percent at a distance of 2 mm downstream from the catheter, and by as much as 25 percent at a distance of 10 mm. This means the velocity measured with an ultrasound catheter does not show the maximum velocity of the undisturbed flow in the tube center. In the constriction, however, the measured velocities with the LDA and ultrasound catheter are almost the same. Thus, catheter measurements in the stenosis achieve accurate results. The velocity profile in the stenosed areas is flattened over nearly the whole cross section. The velocity is extremely reduced only close to the wall. The measurements outside of the stenosis lead to large differences which need to be studied carefully in the future. The disturbed flow finally disappeared 15 mm downstream of the catheter. The measurements were done at steady flow using a glycerine water solution with a dynamic viscosity of 4.35m Pas. In future studies, these experiments will be repeated for pulsatile flow conditions using non-Newtonian blood-like fluids.

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