Abstract: The present investigation aims to study the effect of channel bed slopes on energy dissipation across the different types of Piano Key Weir (PK weir or PKW) under the free-flow conditions in rigid rectangular channels. To this end, three different types (type-A, type-B, and type-C) of PKW models were tested and examined. To document and quantify this experimental investigation, a total of 270 tests were performed, including detailed observations of the flow field. The results show that the energy dissipation of all PKW models increases with the bed slopes and decreases with increasing the discharge over the weirs. In addition, the energy dissipation over the PKW varies significantly with the geometry of the weir. The type-A PKW has shown the highest energy dissipation than the other PKWs. As the bottom slope changed from Sb = 0% to 1.25%, the energy dissipation increased by about 8.5%, 9.1%, and 10.55% for type-A, type-B, and type-C, respectively.
Abstract: Prediction of wall shear stress in a rectangular channel, with non-homogeneous roughness distribution, was studied. Estimation of shear stress is an important subject in hydraulic engineering, since it affects the flow structure directly. In this study, the Genetic Algorithm Artificial (GAA) neural network is introduced as a hybrid methodology of the Artificial Neural Network (ANN) and modified Genetic Algorithm (GA) combination. This GAA method was employed to predict the wall shear stress. Various input combinations and transfer functions were considered to find the most appropriate GAA model. The results show that the proposed GAA method could predict the wall shear stress of open channels with high accuracy, by Root Mean Square Error (RMSE) of 0.064 in the test dataset. Thus, using GAA provides an accurate and practical simple-to-use equation.
Abstract: The aim of this paper is to perform, by mean of the finite volume method, a numerical solution of the transient natural convection in a narrow rectangular channel between two vertical parallel Material Testing Reactor (MTR)-type fuel plates, imposed under a heat flux with a cosine shape to determine the margin of the nuclear core power at which the natural convection cooling mode can ensure a safe core cooling, where the cladding temperature should not reach a specific safety limits (90 °C). For this purpose, a computer program is developed to determine the principal parameters related to the nuclear core safety, such as the temperature distribution in the fuel plate and in the coolant (light water) as a function of the reactor core power. Throughout the obtained results, we noticed that the core power should not reach 400 kW, to ensure a safe passive residual heat removing from the nuclear core by the upward natural convection cooling mode.
Abstract: The aim of this paper is to perform a thermal-hydraulic analysis of the IAEA 10 MW benchmark reactor solving analytically and numerically, by mean of the finite volume method, respectively the steady state and transient forced convection in rectangular narrow channel between two parallel MTR-type fuel plates, imposed under a cosine shape heat flux. A comparison between both solutions is presented to determine the minimal coolant velocity which can ensure a safe reactor core cooling, where the cladding temperature should not reach a specific safety limit 90 °C. For this purpose, a computer program is developed to determine the principal parameter related to the nuclear core safety, such as the temperature distribution in the fuel plate and in the coolant (light water) as a function of the inlet coolant velocity. Finally, a good agreement is noticed between the both analytical and numerical solutions, where the obtained results are displayed graphically.
Abstract: The aim of this paper is to perform an analytic solution of steady state natural convection in a narrow rectangular channel between two vertical parallel MTR-type fuel plates, imposed under a cosine shape heat flux to determine the margin of the nuclear core power at which the natural convection cooling mode can ensure a safe core cooling, where the cladding temperature should not be reach the specific safety limits (90 °C). For this purpose, a simple computer program is developed to determine the principal parameter related to the nuclear core safety such as the temperature distribution in the fuel plate and in the coolant (light water) as a function of the reactor power. Our results are validated throughout a comparison against the results of another published work, which is considered like a reference of this study.
Abstract: Critical depth meters, such as abroad crested weir, Venture Flume and combined control flume are standard devices for measuring flow in open channels. The discharge relation for these devices cannot be solved directly, but it needs iteration process to account for the approach velocity head. In this paper, analytical solution was developed to calculate the discharge in a combined critical depth-meter namely, a hump combined with lateral contraction in rectangular channel with subcritical approach flow including energy losses. Also analytical formulae were derived for approach velocity head coefficient for different types of critical depth meters. The solution was derived by solving a standard cubic equation considering energy loss on the base of trigonometric identity. The advantage of this technique is to avoid iteration process adopted in measuring flow by these devices. Numerical examples are chosen for demonstration of the proposed solution.
Abstract: When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.
Abstract: The present work aims to investigate numerically the thermal and flow characteristics of a rectangular latent heat storage unit (LHSU) during the melting process of a phase change material (PCM). The LHSU consists of a number of vertical and identical plates of PCM separated by rectangular channels. The melting process is initiated when the LHSU is heated by a heat transfer fluid (HTF: water) flowing in channels in a downward or upward direction. The proposed study is motivated by the need to optimize the thermal performance of the LHSU by accelerating the charging process. A mathematical model is developed and a fixed-grid enthalpy formulation is adopted for modeling the melting process coupling with convection-conduction heat transfer. The finite volume method was used for discretization. The obtained numerical results are compared with experimental, analytical and numerical ones found in the literature and reasonable agreement is obtained. Thereafter, the numerical investigations were carried out to highlight the effects of the HTF flow direction and the aspect ratio of the PCM slabs on the heat transfer characteristics and thermal performance enhancement of the LHSU.
Abstract: This numerical study investigates the travelling wave’s appearance and the behavior of Poiseuille-Rayleigh-Benard (PRB) flow induced in 3D thermosolutale mixed convection (TSMC) in horizontal rectangular channels. The governing equations are discretized by using a control volume method with third order Quick scheme in approximating the advection terms. Simpler algorithm is used to handle coupling between the momentum and continuity equations. To avoid the excessively high computer time, full approximation storage (FAS) with full multigrid (FMG) method is used to solve the problem. For a broad range of dimensionless controlling parameters, the contribution of this work is to analyzing the flow regimes of the steady longitudinal thermoconvective rolls (noted R//) for both thermal and mass transfer (TSMC). The transition from the opposed volume forces to cooperating ones, considerably affects the birth and the development of the longitudinal rolls. The heat and mass transfers distribution are also examined.
Abstract: Melting of Paraffin Wax (P116) dispersed with Al2O3 nanoparticles in a rectangular latent heat storage unit (LHSU) is numerically investigated. The storage unit consists of a number of vertical and identical plates of nano-enhanced phase change material (NEPCM) separated by rectangular channels in which heat transfer fluid flows (HTF: Water). A two dimensional mathematical model is considered to investigate numerically the heat and flow characteristics of the LHSU. The melting problem was formulated using the enthalpy porosity method. The finite volume approach was used for solving equations. The effects of nanoparticles’ volumetric fraction and the Reynolds number on the thermal performance of the storage unit were investigated.
Abstract: The exploitation of flow pulsation in micro- and
mini-channels is a potentially useful technique for enhancing cooling
of high-end photonics and electronics systems. It is thought that
pulsation alters the thickness of the hydrodynamic and thermal
boundary layers, and hence affects the overall thermal resistance
of the heat sink. Although the fluid mechanics and heat transfer
are inextricably linked, it can be useful to decouple the parameters
to better understand the mechanisms underlying any heat transfer
enhancement. Using two-dimensional, two-component particle image
velocimetry, the current work intends to characterize the heat transfer
mechanisms in pulsating flow with a mean Reynolds number of
48 by experimentally quantifying the hydrodynamics of a generic
liquid-cooled channel geometry. Flows circulated through the test
section by a gear pump are modulated using a controller to achieve
sinusoidal flow pulsations with Womersley numbers of 7.45 and
2.36 and an amplitude ratio of 0.75. It is found that the transient
characteristics of the measured velocity profiles are dependent on the
speed of oscillation, in accordance with the analytical solution for
flow in a rectangular channel. A large velocity overshoot is observed
close to the wall at high frequencies, resulting from the interaction
of near-wall viscous stresses and inertial effects of the main fluid
body. The steep velocity gradients at the wall are indicative of
augmented heat transfer, although the local flow reversal may reduce
the upstream temperature difference in heat transfer applications.
While unsteady effects remain evident at the lower frequency, the
annular effect subsides and retreats from the wall. The shear rate at
the wall is increased during the accelerating half-cycle and decreased
during deceleration compared to steady flow, suggesting that the flow
may experience both enhanced and diminished heat transfer during
a single period. Hence, the thickness of the hydrodynamic boundary
layer is reduced for positively moving flow during one half of the
pulsation cycle at the investigated frequencies. It is expected that the
size of the thermal boundary layer is similarly reduced during the
cycle, leading to intervals of heat transfer enhancement.
Abstract: The aim of this study is to examine, through
experimentation in the laboratory, the supercritical flow in the
presence of an obstacle in a rectangular channel. The supercritical
regime in the whole hydraulic channel is achieved by adding a
convergent. We will observe the influence of the obstacle shape and
dimension on the characteristics of the supercritical flow, mainly the
free-surface elevation and the velocity profile. The velocity
measurements have been conducted with the one dimension laser
anemometry technique.
Abstract: In this study the augmentation of heat transfer in a rectangular channel with triangular vortex generators is evaluated. The span wise averaged Nusselt number, mean temperature and total heat flux are compared with and without vortex generators in the channel at a blade angle of 30° for Reynolds numbers 800, 1200, 1600, and 2000. The use of vortex generators increases the span wise averaged Nusselt number compared to the case without vortex generators considerably. At a particular blade angle, increasing the Reynolds number results in an enhancement in the overall performance and span wise averaged Nusselt number was found to be greater at particular location for larger Reynolds number. The total heat flux from the bottom wall with vortex generators was found to be greater than that without vortex generators and the difference increases with increase in Reynolds number.
Abstract: Two-dimensional Eulerian (volume-averaged) continuity and momentum equations governing multi-size slurry flow through pump casings are solved by applying a penalty finite element formulation. The computational strategy validated for multi-phase flow through rectangular channels is adapted to the present study. The flow fields of the carrier, mixture and each solids species, and the concentration field of each species are determined sequentially in an iterative manner. The eddy viscosity field computed using Spalart-Allmaras model for the pure carrier phase is modified for the presence of particles. Streamline upwind Petrov-Galerkin formulation is used for all the momentum equations for the carrier, mixture and each solids species and the concentration field for each species. After ensuring mesh-independence of solutions, results of multi-size particulate flow simulation are presented to bring out the effect of bulk flow rate, average inlet concentration, and inlet particle size distribution. Mono-size computations using (1) the concentration-weighted mean diameter of the slurry and (2) the D50 size of the slurry are also presented for comparison with multi-size results.
Abstract: In the study the influence of the physical-chemical properties of a liquid, the width of a channel gap and the superficial liquid and gas velocities on the patterns formed during two phase flows in vertical, narrow mini-channels was investigated. The research was performed in the channels of rectangular cross-section and of dimensions: 15 x 0.65 mm and 7.5 x 0.73 mm. The experimental data were compared with the published criteria of the transitions between the patterns of two-phase flows.
Abstract: Bubble generation was observed using a high-speed
camera in subcooled flow boiling at low void fraction. Constant heat
flux was applied on one side of an upward rectangular channel to
make heated test channel. Water as a working fluid from high
subcooling to near saturation temperature was injected step by step to
investigate bubble behavior during void development. Experiments
were performed in two different pressures condition close to 2bar and
4bar. It was observed that in high subcooling when boiling was
commenced, bubble after nucleation departed its origin and slid
beside heated surface. In an observation window mean release
frequency of bubble fb,mean, nucleation site Ns and mean bubble
volume Vb,mean in each step of experiments were measured to
investigate wall vaporization rate. It was found that in proximity of
PNVG vaporization rate was increased significantly in compare with
condensation rate which remained in low value.
Abstract: A numerical study on the turbulent flow and heat
transfer characteristics in the rectangular channel with different types
of baffles is carried out. The inclined baffles have the width of 19.8
cm, the square diamond type hole having one side length of 2.55 cm,
and the inclination angle of 5o. Reynolds number is varied between
23,000 and 57,000. The SST turbulence model is applied in the
calculation. The validity of the numerical results is examined by the
experimental data. The numerical results of the flow field depict that
the flow patterns around the different baffle type are entirely different
and these significantly affect the local heat transfer characteristics.
The heat transfer and friction factor characteristics are significantly
affected by the perforation density of the baffle plate. It is found that
the heat transfer enhancement of baffle type II (3 hole baffle) has the
best values.
Abstract: In order to obtain an accurate result of the heat transfer
of the rib in the internal cooling Rectangular channel, using separation
of variables, analytical solutions of three dimensional steady-state heat
conduction in rectangular ribs are given by solving three dimensional
steady-state function of the rectangular ribs. Therefore, we can get
solution of three dimensional temperature field in the rib. Based on the
solution, we can get how the Bi number affected on heat transfer.
Furthermore, comparisons of the analytical and numerical results
indicate agreement on temperature field in the rib.
Abstract: The electrokinetic flow resistance (electroviscous
effect) is predicted for steady state, pressure-driven liquid flow at
low Reynolds number in a microfluidic contraction of rectangular
cross-section. Calculations of the three dimensional flow are
performed in parallel using a finite volume numerical method. The
channel walls are assumed to carry a uniform charge density and the
liquid is taken to be a symmetric 1:1 electrolyte. Predictions are
presented for a single set of flow and electrokinetic parameters. It is
shown that the magnitude of the streaming potential gradient and the
charge density of counter-ions in the liquid is greater than that in
corresponding two-dimensional slit-like contraction geometry. The
apparent viscosity is found to be very close to the value for a
rectangular channel of uniform cross-section at the chosen Reynolds
number (Re = 0.1). It is speculated that the apparent viscosity for the
contraction geometry will increase as the Reynolds number is
reduced.
Abstract: This paper analytically investigates the 3D flow
pattern at the confluences of two rectangular channels having 900
angles using Navier-Stokes equations based on Reynolds Stress
Turbulence Model (RSM). The equations are solved by the Finite-
Volume Method (FVM) and the flow is analyzed in terms of steadystate
(single-phased) conditions. The Shumate experimental findings
were used to test the validity of data. Comparison of the simulation
model with the experimental ones indicated a close proximity
between the flow patterns of the two sets. Effects of the discharge
ratio on separation zone dimensions created in the main-channel
downstream of the confluence indicated an inverse relation, where a
decrease in discharge ratio, will entail an increase in the length and
width of the separation zone. The study also found the model as a
powerful analytical tool in the feasibility study of hydraulic
engineering projects.