This paper presents a Monotonic Unbounded Schemes Transformer (MUST) approach to bound/monotonize (remove undershoots and overshoots) unbounded spatial differencing schemes…
Abstract
Purpose
This paper presents a Monotonic Unbounded Schemes Transformer (MUST) approach to bound/monotonize (remove undershoots and overshoots) unbounded spatial differencing schemes automatically, and naturally. Automatically means the approach (1) captures the critical cell Peclet number when an unbounded scheme starts to produce physically unrealistic solution automatically, and (2) removes the undershoots and overshoots as part of the formulation without requiring human interventions. Naturally implies, all the terms in the discretization equation of the unbounded spatial differencing scheme are retained.
Design/methodology/approach
The authors do not formulate new higher-order scheme. MUST transforms an unbounded higher-order scheme into a bounded higher-order scheme.
Findings
The solutions obtained with MUST are identical to those without MUST when the cell Peclet number is smaller than the critical cell Peclet number. For cell Peclet numbers larger than the critical cell Peclet numbers, MUST sets the nodal values to the limiter value which can be derived for the problem at-hand. The authors propose a way to derive the limiter value. The authors tested MUST on the central differencing scheme, the second-order upwind differencing scheme and the QUICK differencing scheme. In all cases tested, MUST is able to (1) capture the critical cell Peclet numbers; the exact locations when overshoots and undershoots occur, and (2) limit the nodal value to the value of the limiter values. These are achieved by retaining all the discretization terms of the respective differencing schemes naturally and accomplished automatically as part of the discretization process. The authors demonstrated MUST using one-dimensional problems. Results for a two-dimensional convection–diffusion problem are shown in Appendix to show generality of MUST.
Originality/value
The authors present an original approach to convert any unbounded scheme to bounded scheme while retaining all the terms in the original discretization equation.
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The purpose of this study is to develop a new method of lines for one-dimensional (1D) advection-reaction-diffusion (ADR) equations that is conservative and provides piecewise…
Abstract
Purpose
The purpose of this study is to develop a new method of lines for one-dimensional (1D) advection-reaction-diffusion (ADR) equations that is conservative and provides piecewise analytical solutions in space, compare it with other finite-difference discretizations and assess the effects of advection and reaction on both 1D and two-dimensional (2D) problems.
Design/methodology/approach
A conservative method of lines based on the piecewise analytical integration of the two-point boundary value problems that result from the local solution of the advection-diffusion operator subject to the continuity of the dependent variables and their fluxes at the control volume boundaries is presented. The method results in nonlinear first-order, ordinary differential equations in time for the nodal values of the dependent variables at three adjacent grid points and triangular mass and source matrices, reduces to the well-known exponentially fitted techniques for constant coefficients and equally spaced grids and provides continuous solutions in space.
Findings
The conservative method of lines presented here results in three-point finite difference equations for the nodal values, implicitly treats the advection and diffusion terms and is unconditionally stable if the reaction terms are implicitly treated. The method is shown to be more accurate than other three-point, exponentially fitted methods for nonlinear problems with interior and/or boundary layers and/or source/reaction terms. The effects of linear advection in 1D reacting flow problems indicates that the wave front steepens as it approaches the downstream boundary, whereas its back corresponds to a translation of the initial conditions; for nonlinear advection, the wave front exhibits steepening but the wave back shows a linear dependence on space. For a system of two nonlinearly coupled, 2D ADR equations, it is shown that a counter-clockwise rotating vortical field stretches the spiral whose tip drifts about the center of the domain, whereas a clock-wise rotating one compresses the wave and thickens its arms.
Originality/value
A new, conservative method of lines that implicitly treats the advection and diffusion terms and provides piecewise-exponential solutions in space is presented and applied to some 1D and 2D advection reactions.
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M. Ravichandran and V. Ganesan
Computation have been made of the three‐dimensional flow fielddevelopment, chemical reaction and combustion processes in a typicalafterburner system under both isothermal and…
Abstract
Computation have been made of the three‐dimensional flow field development, chemical reaction and combustion processes in a typical afterburner system under both isothermal and reacting flow conditions. The calculations are based upon a numerical solution of the time‐averaged transport equations for mass, momentum, turbulence kinetic energy, dissipation rate, enthalpy and species concentrations using a finite‐volume formulation. The physical models include the k—ε turbulence model, the eddy break‐up model, a two‐step reaction model, a droplet vaporization and combustion model and six‐flux radiation model. The mean flow structures are presented in important longitudinal and cross‐sectional planes which show certain striking similarities and contrasting differences for isothermal and reacting flows. The flame stabilizer flow is shown to be dominated by a complex combination of recirculation and vortex patterns. Combustion alters convergence and mixing flow patterns downstream of the flame stabilizer, thus influencing the selection of the fuel injection system. The predicted reacting flow parameters identify a number of design parameters such as fuel injector location, high degree reaction zone, nozzle opening area and the corresponding fuel flow rate.
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DEAR SIR, It is doubtful whether great practical importance can be attached to the precise location of the sonic section in a de Laval nozzle with friction present, under the…
Abstract
DEAR SIR, It is doubtful whether great practical importance can be attached to the precise location of the sonic section in a de Laval nozzle with friction present, under the assumptions of the one‐dimensional theory of flow. The truth of the matter, however, is that the equations of this approximation do lead to the conclusion that the condition of M 1, where M is the Mach number, prevails in the throat of a convergent‐divergent nozzle only in the limiting case of no friction, contrary to Mr Spalding's assertion in the August issue of AIRCRAFT ENGINEERING. It can occur in a section for which dA/dx 0 only if that section is at the exit of a convergent nozzle.
Chandan Kumawat, Bhupendra Kumar Sharma, Taseer Muhammad and Liaqat Ali
The purpose of this study is to determine the impact of two-phase power law nanofluid on a curved arterial blood flow under the presence of ovelapped stenosis. Over the past…
Abstract
Purpose
The purpose of this study is to determine the impact of two-phase power law nanofluid on a curved arterial blood flow under the presence of ovelapped stenosis. Over the past couple of decades, the percentage of deaths associated with blood vessel diseases has risen sharply to nearly one third of all fatalities. For vascular disease to be stopped in its tracks, it is essential to understand the vascular geometry and blood flow within the artery. In recent scenarios, because of higher thermal properties and the ability to move across stenosis and tumor cells, nanoparticles are becoming a more common and effective approach in treating cardiovascular diseases and cancer cells.
Design/methodology/approach
The present mathematical study investigates the blood flow behavior in the overlapped stenosed curved artery with cylinder shape catheter. The induced magnetic field and entropy generation for blood flow in the presence of a heat source, magnetic field and nanoparticle (Fe3O4) have been analyzed numerically. Blood is considered in artery as two-phases: core and plasma region. Power-law fluid has been considered for core region fluid, whereas Newtonian fluid is considered in the plasma region. Strongly implicit Stone’s method has been considered to solve the system of nonlinear partial differential equations (PDE’s) with 10–6 tolerance error.
Findings
The influence of various parameters has been discussed graphically. This study concludes that arterial curvature increases the probability of atherosclerosis deposition, while using an external heating source flow temperature and entropy production. In addition, if the thermal treatment procedure is carried out inside a magnetic field, it will aid in controlling blood flow velocity.
Originality/value
The findings of this computational analysis hold great significance for clinical researchers and biologists, as they offer the ability to anticipate the occurrence of endothelial cell injury and plaque accumulation in curved arteries with specific wall shear stress patterns. Consequently, these insights may contribute to the potential alleviation of the severity of these illnesses. Furthermore, the application of nanoparticles and external heat sources in the discipline of blood circulation has potential in the medically healing of illness conditions such as stenosis, cancer cells and muscular discomfort through the usage of beneficial effects.
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The paper is mainly concerned with how the gas‐turbine designer can choose the best design of liquid or gaseous fuel combustion chamber for his purpose. In the method proposed…
Abstract
The paper is mainly concerned with how the gas‐turbine designer can choose the best design of liquid or gaseous fuel combustion chamber for his purpose. In the method proposed, combustion chamber test data are expressed in a way which gives the most general information about the design, by introducing dimensionless performance criteria. These criteria are then plotted in ways which enable the various chamber designs to be compared. The treatment deals implicitly with the conditions which satisfactory model tests must fulfil. An idealized model of a gas‐turbine combustion chamber is introduced in the light of which the effects of changes in overall fuel/air ratio can be explained more satisfactorily than when conditions in the flame‐tube are supposed homogeneous.
Francisco-Javier Granados-Ortiz, Joaquin Ortega-Casanova and Choi-Hong Lai
Impinging jets have been widely studied, and the addition of swirl has been found to be beneficial to heat transfer. As there is no literature on Reynolds-averaged Navier Stokes…
Abstract
Purpose
Impinging jets have been widely studied, and the addition of swirl has been found to be beneficial to heat transfer. As there is no literature on Reynolds-averaged Navier Stokes equations (RANS) nor experimental data of swirling jet flows generated by a rotating pipe, the purpose of this study is to fill such gap by providing results on the performance of this type of design.
Design/methodology/approach
As the flow has a different behaviour at different parts of the design, the same turbulent model cannot be used for the full domain. To overcome this complexity, the simulation is split into two coupled stages. This is an alternative to use the costly Reynold stress model (RSM) for the rotating pipe simulation and the SST k-ω model for the impingement.
Findings
The addition of swirl by means of a rotating pipe with a swirl intensity ranging from 0 up to 0.5 affects the velocity profiles, but has no remarkable effect on the spreading angle. The heat transfer is increased with respect to a non-swirling flow only at short nozzle-to-plate distances H/D < 6, where H is the distance and D is the diameter of the pipe. For the impinging zone, the highest average heat transfer is achieved at H/D = 5 with swirl intensity S = 0.5. This is the highest swirl studied in this work.
Research limitations/implications
High-fidelity simulations or experimental analysis may provide reliable data for higher swirl intensities, which are not covered in this work.
Practical implications
This two-step approach and the data provided is of interest to other related investigations (e.g. using arrays of jets or other surfaces than flat plates).
Originality/value
This paper is the first of its kind RANS simulation of the heat transfer from a flat plate to a swirling impinging jet flow issuing from a rotating pipe. An extensive study of these computational fluid dynamics (CFD) simulations has been carried out with the emphasis of splitting the large domain into two parts to facilitate the use of different turbulent models and periodic boundary conditions for the flow confined in the pipe.
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To the Editor. DEAR SIR, In the June issue of AIRCRAFT ENGINEERING, Mr V. D. Naylor rightly asserts that, according to one‐dimensional theory, the velocity at the throat of a…
Abstract
To the Editor. DEAR SIR, In the June issue of AIRCRAFT ENGINEERING, Mr V. D. Naylor rightly asserts that, according to one‐dimensional theory, the velocity at the throat of a Laval nozzle is the local sonic velocity, whether friction is present or not. However his proof rests on an expansion law pvn=constant, when n≠y, and the throat velocity which he obtains differs according to the value of n. Both the assumption and the conclusion are false. The confusion which has existed on this point is, therefore, deepened.
Keivan Khademi Shamami and Madjid Birouk
This paper aims to describe the numerical simulation of a three‐dimensional turbulent free jet issuing from a sharp‐edged equilateral triangular orifice into still air.
Abstract
Purpose
This paper aims to describe the numerical simulation of a three‐dimensional turbulent free jet issuing from a sharp‐edged equilateral triangular orifice into still air.
Design/Methodology/approach
The numerical simulation was carried out by solving the governing three‐dimensional Reynolds‐averaged Navier‐Stokes equations. Several two‐equation eddy‐viscosity models (i.e. the standard k‐ε, renormalization group (RNG) k‐ε, realizable k‐ε, shear‐stress transport (SST) k‐ω), as well as the Reynolds stress models (i.e. the standard RSM and the SSG) were tested to simulate the flowfield. The numerical predictions were compared with experimental data in order to assess the capability and limitations of the various turbulent models examined in this work. Findings –The vena contracta effect was predicted by all the tested models. Among the eddy‐viscosity models only the realizable k‐ε model showed good agreement of the near‐field jet decay. None of the eddy‐viscosity models was capable of predicting the profiles of the jet turbulence intensities. The RSMs, especially the standard RSM, were able to produce much better predictions of the features of the jet in comparison with the eddy‐viscosity models. The standard RSM predictions were found to agree reasonably well with the experimental data.
Research limitations/implications
The conclusion, that among the tested RANS turbulence closure models, the RSM appeared the only one capable of reproducing reasonably well the experimental data concerns only the jet flow case examined here. Also, the average computational time for a single run was quite long, i.e. 340 h, but it is believed that parallel computing will reduce it considerably.
Originality/value
The numerical results reported in this paper provide a comparison between several RANS turbulence closure models for simulating a turbulent free jet issuing from an equilateral triangular nozzle.
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Jaime Alvarez, Mirko Pap and Alvaro Valencia
This work numerically investigates the effects of two square bars placed in various arrangements in a channel on pressure drop and heat transfer. Tandem arrangements and the two…
Abstract
This work numerically investigates the effects of two square bars placed in various arrangements in a channel on pressure drop and heat transfer. Tandem arrangements and the two bars arranged side by side to the approaching flow are considered. The separation distance between the bars is varied in both types of arrangements. The Reynolds number Re based on channel height is 104, whereas the bar height to channel height (d/H) is 0.152. The channel walls are subjected to a constant wall temperature. The k‐ε turbulence model was used in conjunction with the Reynolds‐averaged momentum and energy equations for the simulations. A finite volume technique with staggered grids combined with the SIMPLEC algorithm is applied with a fine grid resolution. Results show that the local and global Nusselt numbers on the channel walls are strongly increased by the unsteady vortex shedding induced by the bars.