Forthcoming articles

Progress in Computational Fluid Dynamics, An International Journal

Progress in Computational Fluid Dynamics, An International Journal (PCFD)

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Progress in Computational Fluid Dynamics, An International Journal (23 papers in press)

Regular Issues

  • Fluid-Structure Interaction Analysis of the Return Pipeline in the High-Pressure and Large-Flow-Rate Hydraulic Power System   Order a copy of this article
    by Yong Sang, Pengkun Liu, Xudong Wang, Weiqi Sun, Jianlong Zhao 
    Abstract: In order to investigate the static and dynamic characteristic of the return pipeline in the high-pressure and large-flow-rate hydraulic power system and avoid pipeline vibration, the geometry model of a simply supported pipeline connected to a sliding valve is established and a one-way coupling fluid-structure method is introduced to study the return pipeline vibration. First, the modal analyses with an empty pipeline and a pipeline filled with water are performed and compared. Pipeline resonance phenomenon is investigated with the prescribed fluctuating flow and the pipeline response frequency is achieved by FFT analysis. Then, the corresponding modal experiment is performed. The calculated and experimental results are proved to be consistent. In the end, the return pipeline dynamic transient response is simulated and the dynamic mesh and UDF are combined in Fluent when the sliding valve is open. The return pipeline vibration and water hammer phenomenon are observed. The analysis of the dynamic characteristics under the influence of the fluid velocity and the pipeline wall thickness is carried out. The results show that the flow induced pipeline vibration caused by the valve opening cant be lightened effectively by reducing the fluid inlet velocity, but can be greatly mitigated by increasing the pipeline wall thickness.
    Keywords: Fluid-Structure interaction; pipeline; vibration; coupling; water hammer; sliding valve.

  • A switching ILU(0)-SGS preconditioner for matrix systems of incompressible flow and heat transfer using condition number estimates   Order a copy of this article
    by Krishna Chandran, Krishnamurthy Muralidhar 
    Abstract: Preconditioning strategies for pressure-velocity-temperature matrix systems obtained from an unstructured finite volume discretization of the three-dimensional incompressible flow and thermal energy equations are studied by reference to their condition numbers. The computational procedure for determining the exact condition number is expensive and is circumvented by providing Gershgorin-type theoretical bounds available for diagonally dominant matrices. The discretized system of linear algebraic equations of mass, momentum, and temperature are solved using the preconditioned-BiCGSTAB algorithm. Condition numbers of velocity and temperature matrices obtained from the Gershgorin-type estimates show these to be well-conditioned compared to pressure. As a result, for the well-conditioned matrices the symmetric Gauss Seidel (SGS) preconditioner performs well on single and multi-processor architectures when compared to ILU(0) that requires additional LU factorization. Based on numerical experiments, the present study proposes a preconditioning algorithm that switches from ILU(0) to SGS preconditioner for the well-conditioned matrices based on the Gershgorin-type condition number estimates. The composite algorithm shows a reduction in the overall simulation time for flow and mixed convection inside a 3D differentially heated cavity. The present study also shows that the Gershgorin based upper bounds for the largest singular value capture the transition details of flow dynamics in several applications. For developing flow of a power law fluid in a tube, the upper bound correlates with the power law index. For flow past a circular cylinder, the time-wise oscillation of the theoretical bound of the largest singular value predicts the onset of vortex shedding.
    Keywords: Unstructured finite volume method; singular values; condition number; Gershgorin estimates; switching preconditioning.

  • Flow Instability of Two-Parallel Moving Walls in Cubical Cavity Induced by an Inner Cylindrical Shape at Different Radii Sizes   Order a copy of this article
    by Basma Souayeh, Fayçal Hammami 
    Abstract: A computational analysis has been performed to study the flow instability of two-parallel wall motions in a cubical cavity incorporated by a cylindrical shape under different radii sizes. A numerical methodology based on the Finite Volume Method and a full Multigrid acceleration is utilized in this paper. Left and right parallel walls of the cavity are maintained driven and all the other walls completing the domain are motionless. Different radii sizes (R=0.075, 0.1, 0.125, 0.15 and 0.175) are employed encompassing descriptive Reynolds numbers that range three orders of magnitude 100, 400 and 800 for the steady state. The obtained results show that positions R=0.15 and R=0.175 of the inner cylinder promote cell distortion. Also, when the radius equates to R=0.15, that may lead to the birth of tertiary cells at Re=400 which are more developed for Re=800. Thereafter, analysis of the flow evolution shows that with increasing Re beyond a certain critical value, the flow become unstable and undergoes a Hopf bifurcation. A non-uniform variation with the radius size of the inner cylinder is observed. Otherwise said, by elongating the radius of the cylinder, that leads to decrease the critical Reynolds number, hence, the acceleration of the unsteadiness. On the other hand, by further increasing Reynolds number more than the critical value from 1200 to 2100, we note that the kinetic energy is monotonously increasing with Reynolds number and a stronger motion in the velocity at the level of the rear wall of the cavity is observed. Furthermore, the symmetry of flow patterns observed in the steady state has been lost. Therefore, a systematic description of various effects illuminating the optimum geometrical parameters to achieve effective flow behavior in those systems has been successfully established through this paper.
    Keywords: Computational analysis; Cylindrical shape; Lid-driven cavity; Two-parallel wall motions; Cylinder radius.

  • Supercritical carbon dioxide turbomachinery development using scaling methodology, computational fluid dynamics and experimental testing in aeroloop   Order a copy of this article
    by Vijajaraj K, Punit Singh 
    Abstract: Supercritical carbon dioxide (SCO2) turbomachinery design experience is limited. This paper examines similarity-based scaling strategy to develop a radial inflow turbine and centrifugal compressor from existing proven designs for a 50kWe SCO2 Brayton cycle. The SCO2 turbine and compressor are developed from well-established NASA 1730 air turbine and NASA 4613 radial pump, respectively. Computational fluid dynamic (CFD) simulations with air and SCO2 and experimental testing in aeroloop are carried out for the developed turbomachinery. The results are compared with original NASA test data. For the turbine, the CFD simulation and experimental results were in good agreement with NASA data. For the compressor, CFD simulation results with SCO2 showed good conformance especially the, efficiency values, which were much lower for air. The compressor experimental results were well away from the NASA data when head rise coefficient was considered, but the flow coefficient zone coincided with that of simulation
    Keywords: Supercritical carbon dioxide Brayton cycle; Scaling; CFD; Turbine; Compressor.

  • Aerodynamics of symmetric permeable airfoils and wings: CFD Simulation   Order a copy of this article
    by Mohammed Aldheeb, Waqar Asrar, Afaq Altaf, Ashraf Omar, Erwin Sulaeman 
    Abstract: This paper presents a simple, and effective CFD modelling of a permeable thin symmetric airfoil and a wing based on the profile of NACA 0008 at a chord-based Reynolds number of 3.45
    Keywords: Permeability; Permeable Airfoil; Permeable Wing; Aerodynamics; Porosity.

  • Evaluation of Dynamic Impact of Flow with Bridge Pier Using Smoothed Particle Hydrodynamics Method   Order a copy of this article
    by Tu Anh Do, Thuan Huu Nguyen, Hai Manh Nguyen 
    Abstract: This paper presents a numerical model for the hydrodynamic impact of water flow with a bridge pier placed on a group of piles using the Smoothed Particle Hydrodynamics (SPH) method. A new boundary processing technique using a combination of ghost particles and dynamic boundary particles is implemented in the SPH simulations of this study. The numerical probes are uniformly distributed over the vertical surface of the structure in order to obtain detailed measurements of the flow pressure on the structure over time. Using the SPH simulations, the velocity field of the unstable flow surrounding the piles and the equivalent hydrodynamic force acting on the pile cap are determined. The vulnerable impact locations on the structure surface are also predicted from the time-pressure histories. Additionally, the predicted hydrodynamic pressure values are compared with those proposed by AASHTO (2012) for bridge design considerations.
    Keywords: smoothed particle hydrodynamics; flow impact load; bridge pile cap; pile/pier-flow interaction.

  • Numerical simulation on heat transfer of nanofluid in conical spiral heat exchanger   Order a copy of this article
    by Ali Davoudi, Saeed Daneshmand, Vahid Monfared 
    Abstract: In this research article, the performance of a conical spiral heat exchanger with rectangular cross sections is numerically investigated by using two different nanofluids; aluminum oxide/water (?Al?_2 O_3/Water) and copper oxide/water (CuO/Water) nanofluid. For this purpose, the effects of nanofluid concentration on the secondary flow, pressure drop, heat transfer and figure of merit (FOM) (the ratio of total heat transfer to the required fluid for pumping) are investigated. On the structured grid, the continuity, momentum, and energy equations are solved by employing a finite volume method. Results indicate that by enhancing the concentration of a nanofluid, the formed secondary flow gains more power. Based on the obtained results, the pressure drop increases with enhancing the nanofluid concentration along the tube. The heat transfer rate is slightly increased by adding nanoparticles to the base water fluid in very low concentrations, but with increasing the concentration of nanofluids, the heat transfer rate reduces. Moreover, FOM decreases with increasing nanofluid concentration. This variation is higher for copper oxide compared to alumina nanofluids at lower concentrations, while it is higher for alumina nanofluid at higher concentrations.
    Keywords: Heat exchanger; Numerical simulation; Nanofluid; Heat transfer.

  • Aerodynamic design and computational fluid dynamic analysis of radial outflow turbines for steam Rankine cycle and supercritical carbon dioxide Brayton cycle   Order a copy of this article
    by Vijayaraj Kunniyoor, Karthik Nadella, Punit Singh 
    Abstract: The first part of this paper presents the design of a radial outflow steam turbine for a micro steam power pump block of 200 kW capacity based on a unique Ljungstrom turbine design methodology. Computational Fluid Dynamic (CFD) simulations were carried out for the 18-stage radial outflow steam turbine at design and off-design points, and results proved the validity of the undertaken design methodology. The design point CFD simulation showed a total to total efficiency of 74.4 % for the steam turbine. Specific speed and specific diameter values for the radial outflow steam turbine stages were calculated and superimposed on the Baljes specific speed-specific diameter chart, thus identifying a unique radial outflow turbine zone in the chart. The second part of this paper presents a new design methodology based on specific speed and specific diameter values for designing a supercritical carbon dioxide radial outflow turbine for a 1MW supercritical carbon dioxide (SCO2) Brayton cycle. CFD simulations were carried out at design and off-design points for the SCO2 turbine. The total to total efficiency from the CFD simulation at the design point for the SCO2 turbine is 84.6 %.
    Keywords: Radial outflow turbine; steam; supercritical carbon dioxide; Specific speed-specific diameter chart.

  • Numerical and experimental investigation of sloshing in a water tank with a fully coupled fluid-structure interaction method   Order a copy of this article
    by Abdullah Demir, A. Ersin Dinçer, Sevki Öztürk, Ilker Kazaz 
    Abstract: In the present study, the harmonic movement of fluid flow and the behavior of elastic structure under this movement are investigated. Accordingly, a recently developed fluid-structure interaction method in which fluid and structure are simulated with smoothed particle hydrodynamics (SPH) and finite element method (FEM) is used. The interaction between fluid and the structure is satisfied with contact mechanics. In order to validate the numerical model under harmonic movement, different experiments are used. First, the structure is assumed to be rigid and the pressures calculated on the structure are compared with the experimental data available in literature. Similarly, free-surfaces are also validated with novel experiments carried out in the context of this study. In addition, the interaction between an elastic structure and fluid is investigated in the novel experiments in which a water tank having an elastic buffer in the middle is moved under harmonic horizontal movement and the deflection of the elastic buffer and free-surface profiles are measured. Comprehensive results are given for all validation cases. According to the results, the numerical method is successful and can be used in these type of problems.
    Keywords: Smoothed particle hydrodynamics; contact mechanics; fluid-structure interaction; FSI,;sloshing; elastic buffer.

  • Numerical Study on the Sloshing flows in a Prismatic Tank using Natural Frequency of the Prismatic Shapes   Order a copy of this article
    by Hyunjong Kim, Nanjundan Parthasarathy, Yeon-Won Lee 
    Abstract: In this numerical study, a 2D prismatic tank subjected under horizontal excitation is used to analyze the sloshing characteristics for a specific range of Reynolds number, from 2.5E4 to 2.0E5. Three models of geometric variable delta1, namely, delta1=50mm, delta1=150mm and delta1 =250mm are used to observe the effects of the lower chamfered shape of the prismatic tank, where the Reynolds number for each delta1 ranges from 2.5E4 to 2.0E5 (12 Cases). The Volume of Fluid (VOF) method is used for the multiphase flow analysis. The Fast Fourier Transforms (FFT) technique is used to analyse the frequency components of excitation force and the magnitude of the amplitude spectrum. The results show that the sloshing wave fluctuation becomes small when the geometric variable delta1 is larger. Also, the FFT technique shows that the resonance does not occur due to frequencies which are not integral multiple of the excitation frequency. Moreover, for the sloshing load analysis, the free surface length is an important parameter than the shapes of the lower section.
    Keywords: Sloshing; Reynolds number; VOF method; FFT analysis; CFD; Prismatic tank; Sloshing impact pressure; Two-phase flow.

  • Numerical Simulation and Optimization of a Reinforced Steel Plate against Underwater Explosions   Order a copy of this article
    by Arman Jafari Valdani, Armen Adamian 
    Abstract: Optimum arrangement of reinforcing blades can increase the resistance of marine structures and reduce potential losses in the case of explosive events. In this research, to find the most appropriate arrangement, six different geometries were modeled in 3D (1 base case and 5 cases with different arrangements of reinforcing blades). By using Lagrangian and Eulerian methods for grid generation, the effects of the explosion on these structures in the water environment were simulated, and the variation of the Von-Mises stress, damage parameter, strain, displacement, and displacement rate were predicted for all cases. The simulations were based on finite element-finite volume methods. The accuracy of the numerical approaches was confirmed by analyzing benchmark problems and comparing the obtained results with analytical and experimental data. It was found that maximum damage takes place in case A (plate without any blades) with maximum displacement and displacement rate of 521 mm and 151 mm/ms, respectively. Also, the results of parametric simulations revealed that case F with six perpendicular reinforcing blades was the best arrangement. In this case, the displacement and displacement rate of the plate relative to the base case (without any blades) were reduced by 40% and 64%, respectively.
    Keywords: Numerical Simulation; Explosive Loads; Water Environment; Fluid-Structure Interaction; Reinforcing Blades.

    by Selma Akcay, Unal Akdag 
    Abstract: In this study, the heat transfer performance of an oscillating vertical flat plate is experimentally and numerically investigated. Rayleigh number (Ra), Womersley number (Wo), and dimensionless oscillation amplitude (Ao) are changed, and the effects of these parameters on heat transfer performance are analyzed. The numerical simulations are performed using a finite volume method based Computational Fluid Dynamics procedure, and the numerical results are validated by comparisons with the experiments. To explain the heat transfer mechanism, the instantaneous velocity and temperature profiles on the plate surface are obtained. It has been observed that the periodic oscillations continuously renewed the velocity and thermal boundary layer, increased the convection effects, and improved the heat transfer. Consequently, the heat transfer performance was significantly affected by the oscillation parameters and increased as both Wo and Ao increased for all tested Rayleigh numbers (Ra). The maximum heat transfer improvement achieved was about 45% at a high amplitude (Ao = 1.4) and frequency (Wo = 146) at Rayleigh number (Ra = 1.17
    Keywords: oscillating vertical plate; heat transfer performance; mixed convection.

  • The Galerkin Least Squares MLPG Method for Convection-dominated Problems   Order a copy of this article
    by Xuehong Wu 
    Abstract: Meshless method had been applied widely in the computational mechanics, materials science and computational heat transfer and fluid flow. It is difficult for meshless method to develop the high efficient method for convection term in the computational fluid dynamics. In this paper, a truly meshless method---MLPG (Meshless local Petrov-Galerkin)method is applied to solve convection-diffusion problem, and GLS(Galerkin Least Squares) approximation method is proposed and applied to overcome the influence of convection term, Some cases with benchmark solutions are used to validate the accuracy and efficiency of the present method. The computational results show that GLS method can very good to deal to convection-diffusion problems and has very high computational precise.
    Keywords: Upwind Scheme; GLS method; SUPG method; MLPG method; Meshless method.

  • Role of aspiration to enhance MHD convection in protruded heater cavity   Order a copy of this article
    by Nirmalendu Biswas, Aparesh Datta, Nirmal Kumar Manna, Dipak Kumar Mandal, A.C. Benim 
    Abstract: The implementation of free aspiration of the working fluid can significantly intensify heat transfer in the absence of any fan/pump for low power thermal applications. To explore the effectiveness of aspiration, the present study is devoted to a classical protruded-heater thermal cavity along with the magnetic field. The heater is located centrally at the middle position of the bottom of the cavity. The aspiration openings are provided at the bottom of the sidewalls (for passive and partial suction of working fluid) and in the middle of the top wall (for partial venting). The efficacy of aspiration is assessed with respect to the no-aspiration condition. The magneto-thermal-hydrodynamics in the cavity is captured numerically considering different strengths of the magnetic field and buoyancy and heater sizes. The numerical simulations are performed using an in-house CFD code in dimensionless form for a broad range of Rayleigh number (Ra), Hartmann number (Ha), and heater aspect ratio (A). The evolved results indicate substantial augmentation of heat transfer (even with the absence of any fluid pumping means) obtained from free aspiration. The heat transfer augmentation here could be up to 46% based on the parametric conditions. On the other hand, the imposed magnetic field shows a prominent role in the control of temperature and convective flow in the cavity. The aspiration plays a positive role in heat transfer enhancement under natural convection with and without a magnetic field.
    Keywords: Magneto-hydrodynamic (MHD) flow; Aspiration; Natural convection; protruded heater; Heat transfer augmentation.

  • Efficiency of particle search methods in Smoothed Particle Hydrodynamics: A comparative study (Part I)   Order a copy of this article
    by Eric Plaza, Leoanrdo Di G. Sigalotti, Luis Perez, Jorge Troconis, Wilfredo Angulo, Maria Castro 
    Abstract: Nearest neighbor searching is a fundamental problem in all applications of Smoothed Particle Hydrodynamics (SPH). Here we compare the efficiency of most used searching methods in vectorized form such as the Brute Force (BF) or Direct Search (DS), the cell-linked list (CLL) and the KD-tree (KDT) methods. The time duration of the calculations for the SPH scales as N^2.74 and N^2.45 with the BF and CLL methods, respectively, where N is the total number of particles. In contrast, the Vectorized Brute Force (VBF) method works efficiently only for N<=10000 and scales as N^13.83 for larger N. The results also indicate, as was shown in previous works, that the efficiency of the SPH calculations is greatly improved with the Vectorized cell-linked list (VCLL) and the Vectorized KD-tree (VKDT) methods. However, the VKDT approach is more efficient than the VCLL method for N<= 10^5 in two dimensions (2D) and N<=10^6 in three dimensions (3D). For larger N, the time duration of the SPH calculations with the VKDT method grows steeply (scaling as N^14.53 in 2D and N^6.42 in 3D), while a linear trend is maintained with the VCLL method. The trend of complexity here is measured not only for early events, but also close to the point of hardware limit. The measure of complexity in this limit does not correspond to the trend of early events. So, each method has a different behavior, which can be measured and compared using a power fit.
    Keywords: Nearest neighbor search; Closest pair search; Data structures; Smoothed Particle Hydrodynamics.

  • Finite element simulations of thin films flowing down planes or cylinders   Order a copy of this article
    by Chicheng Ma, Wei Wang, Mingyu Shao, Zonghe Guo 
    Abstract: This paper considers contact line dynamics for liquid films flowing down planes or cylinders. Finite element modeling are introduced based on the open-source finite element software Freefem++. Using the reduced model of thin liquid films, the weak form of the partial differential equations are derived for finite element simulations. Both two-dimensional flow and three-dimensional flow of thin films are numerically simulated and the surface instability is analyzed. The results obtained in this paper show good agreement with the results from the previous investigation. Results show that traveling wave phenomena is found in the time evolution while a unperturbed initial contact line is given. If given small perturbed initial contact line, pattern of viscous fingers appears. The radius of the cylinder plays an important role in the flow pattern, and the number of fingers is approximately linearly with the radius of the cylinder. The proposed method and calculation code are useful for gaining better insight into the thin liquid film problems.
    Keywords: Numerical simulation; cylinder; falling film; finite element method; Freefem++.

  • Extension of an immersed boundary method for large eddy simulation of turbulent flows   Order a copy of this article
    by Tianmei Pu, Chunhua Zhou 
    Abstract: In this paper, an immersed boundary method is extended to large eddy simulation of turbulent flows. For the interior nodes in the immediate vicinity of the immersed wall, some of their neighboring nodes are in the solid phase, and the flow variables at these interior nodes cannot be calculated by solving the governing equations. In the present immersed boundary method, the flow variables at these nodes are determined via an approximate form of solution involving the boundary condition. A wall model based on the simplified turbulent boundary layer equations is introduced to alleviate the requirement of mesh resolution in the near-wall region. The wall shear stress prescribed by the wall modeling technique and the no-penetration condition are enforced at the immersed boundary to evaluate the velocity at an interior node in the immediate vicinity of the wall. A dynamic subgrid-scale model is adopted in the framework of the immersed boundary approach. Several numerical experiments have been conducted to verify the ability of the present method. The predicted results agree well with the published experimental or numerical data.
    Keywords: immersed boundary method; turbulent flows; wall modeling; large eddy simulation; dynamic subgrid-scale model.

  • Numerical simulation of viscoelastic blood flow with hematocrit variation in an arterial segment with two aneurysms   Order a copy of this article
    by Ahmed Elhanafy, Ahmed Elsaid 
    Abstract: In this study, a viscoelastic model with variable viscosity and relaxation-time is proposed for the simulation of the blood flow in an arterial segment with two aneurysms. The Quemada model is adopted to model both the shear rate-dependent viscosity and hematocrit variation. Available experimental data for the shear rate-dependent relaxation-time of the blood, in a certain range, are fitted and used. The arterial segment with aneurysms is considered as a rigid axisymmetric thin tube with two balloon expansions. The stabilized finite element method with the discrete elastic viscous stress splitting method (DEVSS) is used to solve the governing equations to overcome the numerical instabilities. Numerical results including velocity profiles, shear rate distribution and viscosity contours are obtained under different values of red blood cells (RBCs) concentrations. The results indicate that the hematocrit variation has a significant effect on the flow regimes and hemodynamics factors such as the wall shear stress (WSS). Hence the shear thinning property should not be ignored for blood flow simulations.
    Keywords: Abdominal aortic aneurysms; Blood viscoelasticity; DEVSS method; Hematocrit variation; WSS.

  • Experimental and numerical study of upstream slope stability in an earth dam reservoir under rapid drawdown conditions   Order a copy of this article
    by Mansour Pakmanesh, Seyed Habib Mousavi Jahromi, Amir Khosrojerdi, Hossein Hassanpour Darvishi, Hossein Babazadeh 
    Abstract: The rapid water level drawdown of the dam reservoirs is one of important factors of earth dam stabilities. This phenomenon might occur over the lifetime of the earth dams and levees. During the dams exploiting, rapidly decreasing of the reservoir water head causes that the seepage flow has the backward orientation. This backward flow to the dam reservoir where is not commonly considered some contour measurement to avoid the piping phenomenon. This situation increases pore water pressure through the upstream slope of the dam body which can apparently raise the piping potential. This condition can make a critical situation which should be controlled by applying some counter measurements. In order to investigate the effect of the hydraulic conductivity on the rapid drawdown of water level, an experimental model was constructed in experimental flume. By obtaining the hydraulic parameters of the materials, the flow through this model was modeled by seep/w software. The input information into the software model such as hydraulic conductivity and volume water content were provided by preforming some soil mechanical tests such as the constant load and using a disk penetrometer, respectively. After validation of hydraulic conductivity with the numerical model, the results were compared with the observed data. Finally, A good agreement is observed between the experiments and predictions. Furthermore, the saturated and unsaturated simulations indicate that the unsaturated model has a much better agreement with the experimental model. It is found that the unsaturated model is more convenient for the simulation flow through the homogenous earth dam than the saturated model.
    Keywords: Slope Stability; rapid ?drawdown; earth dam; drainage prediction; seep/w.

  • Effect of cross-confinement on unsteady wake characteristics of circular cylinder immersed in shear flow   Order a copy of this article
    by Prashant Kumar, Shaligram Tiwari 
    Abstract: Present study investigates effect of cross-confinement on three-dimensional unsteady wake characteristics in flow past circular cylinder mounted on a surface using OpenFOAM. Aspect ratio (ratio of height to diameter of the cylinder) is kept fixed equal to 4. Temporal wake behavior has been characterized at fixed Reynolds number equal to 200 using Hilbert Huang transformation of transverse velocity signals. Frequency and energy distributions of component signals have been illustrated with the help of Hilbert spectra. Variation in frequency of vortex shedding with the change in shear intensity and top confinement has been illustrated in marginal spectra. Quantification of nonlinear fluctuations in the wake has been presented in terms of degree of stationarity. Spatial and temporal evolutions of vortex modes (frequency and growth rate) have been examined using recently developed snapshot-based technique Dynamic Mode Decomposition (DMD). Periodic behavior of the wake has been illustrated using recurrence plot (RP) and different quantification estimates are presented based on patterns that appear in the RP.
    Keywords: Hilbert spectra; marginal spectra; degree of stationarity; dynamic mode decomposition; recurrence plot.

  • Mathematical formulation for the analysis of the periodic convergence during co-processing routines in long-run, scale-resolving simulations of turbomachinery   Order a copy of this article
    by Jesus Manuel Fernandez Oro 
    Abstract: Scaled-Resolving Simulations, like LES modelling, are recent CFD techniques to analyse numerically unsteady flows and turbulence in turbomachinery. Despite their high computational costs, they provide an unsteady, time-resolved solution of the flow with embedded turbulent scales. From an engineering point-of-view, a statistical description of such solutions is mandatory. Thus, phase-averaged values of velocity fields and turbulent scales must be postprocessed in order to provide a representative description of the unsteadiness, using a minimum number of averages that it is a priori unknown. This required number depends on the flow complexity, the type of turbomachine and its operating condition. In order to save computational costs, the present paper provides the mathematical formulation required to compute and assure that periodic convergence has been met. The framework has been developed to update the phase-averaged values and the residual on the run, so the amount of data to be stored is extremely reduced. Following, the formulation is applied over a previous numerical database concerning a Wall-Modelled LES simulation of the Rotor-Stator Interaction in a low-speed axial fan using a 3D linear cascade model. The results obtained confirm that convergence of turbulent structures is more compromised than primary flow variables due to inherent instabilities of the coherent flow vortices. This work forms part of the concept of co-processing, in which some operations related to post-processing routines are moved towards the iterative resolutions processes of numerical CFD simulations in order to save computational costs.
    Keywords: Statistical convergence; co-processing; phase-averaging; LES simulation; Rotor-Stator interaction; axial fan.

  • Numerical Investigation of Transverse Injection and Mixing with a Mach 3 Supersonic Cross-flow   Order a copy of this article
    by Sagarika Iyer, Viswanath Babu 
    Abstract: Numerical simulations of the transverse injection of helium(surrogate for hydrogen) into a\r\nMach 3 cross-flow through circular and wedge injectors have been carried out. Three-dimensional,\r\ncompressible, steady Favre-averaged Navier-Stokes equations have been solved using the SST k-?\r\nturbulence model. Flow conditions of the injectors are matched to isolate the effect of injector geometry.\r\nMach number contours inside the injector reveal the flow at the exit of the injector to be supersonic and\r\nnot sonic, as it is usually assumed to be. Oil flow visualization shows flow features such as a bow shock\r\nand separated flow regions around the injectors. Shadowgraphs reveal two parallel shock waves\r\noriginating from the injection location as well as the thickening of the boundary later downstream of\r\nthe injector. Helium mass fraction contours on axial planes show the injectant plume and its spreading\r\nin the vertical and spanwise (lateral) direction. Performance metrics such as penetration height and\r\ndegree of mixing of the injectors have been compared. Results show that the circular injector has better\r\nmixing performance when compared to the wedge injector for the operating conditions considered.\r\nResults from the present calculations show reasonable agreement with experimental data from an\r\nearlier study.
    Keywords: Scramjet; supersonic combustion; simulations; injection; mixing.

  • The finite element reliable scheme for the numerical analysis of the Burgers\'-Fisher equation   Order a copy of this article
    by Pius W. Molo Chin 
    Abstract: We consider in this paper, the nonstandard finite difference method in the time variable combined with the finite element method in the space variables. We use this to study the Burgers-Fisher equation which is one of the most important nonlinear partial differential equation appearing in various applications such as in Fluid dynamics. Existence and uniqueness of the solution of the above equation is determined for a given small data on appropriate spaces. The numerical scheme of the problem is proposed using the above combination. The proposed scheme is successfully implemented by firstly establishing the stability of the scheme and secondly by determining the estimate for the optimal convergence rate of the solution of the problem in both the L^2 as well as H^1-norms. Furthermore, we show that the numerical solution of the scheme preserves the decaying properties of the exact solution and numerical experiments with the help of an example is presented to justify the validity of the results
    Keywords: Burgers’-Fisher equation; nonlinear equation; non-standard finite difference method; finite element method; optimal rate of convergence.