Solution Of Fluid Flow Research Articles

Conjugate rotor-stator interaction procedure for film-cooled turbine sections

PurposeThe authors aim to present a procedure for the parallel, steady and unsteady conjugate, Navier–Stokes/heat-conduction rotor-stator interaction analysis of multi-blade-row, film-cooled, turbine airfoil sections. A new grid generation procedure for multiple blade-row configurations, including walls, thermal barrier coatings, plenums, and cooling tubes, is discussed.Design/methodology/approachSteady, multi-blade-row interaction effects on the flow and wall thermal fields are predicted using a Reynolds’s-averaged Navier–Stokes (RANS) simulation in conjunction with an inter-blade-row mixing plane. Unsteady, aero-thermal interaction solutions are determined using time-accurate sliding grids between the stator and rotor with an unsteady RANS model. Non-reflecting boundary condition treatments are utilized in both steady and unsteady approaches at all inlet, exit and inter-blade-row boundaries. Parallelization techniques are also discussed.FindingsThe procedures developed in this research are compared against experimental data from the Air Force Research Laboratory’s turbine research facility.Practical implicationsThe software presented in this paper is useful as both the design and analysis tool for fluid system and turbomachinery engineers.Originality/valueThis research presents a novel approach for the simultaneous solution of fluid flow and heat transfer in film-cooled rotating turbine sections. The software developed in this research is validated against experimental results for 2D flow, and the methods discussed are extendable to 3D.

On the dynamics of the transition to vortex breakdown in axisymmetric inviscid swirling flows

This paper reports on novel features found in the dynamics of the transition to vortex breakdown in inviscid axisymmetric flows with swirl. These features are revealed by a transient simulation of an open ended pipe flow where the inlet swirl is suddenly increased from a swirl number just below the onset of vortex breakdown to a swirl number just above the onset of vortex breakdown. To eliminate the numerous parameters influencing breakdown, the axisymmetric Euler equations with swirl are used as a fluid flow model and solutions are obtained by means of numerical simulation. It is shown that as the step response has died out, the flow evolves to a quasi-static state where time derivatives of variables are negligible small. Stability analysis of this state shows that it can support standing waves in a small region of the flow domain. These standing waves are observed in the simulations as an imbalance in the axial momentum equation which slows down the flow near the central axis. The amplitude of this imbalance grows exponentially in time with a dimensionless growth rate of 0.83 scaled with the flowthrough time. Eventually, the axial velocity along the central axis becomes negative in a small part of the flow, leading to an axisymmetric recirculation zone, called vortex breakdown. To the authors knowledge, this study would be the first to reveal these features prior to breakdown and the results may help in understanding of the physical mechanisms leading to it as this is still a controversial issue in literature.

An approximate solution for the MHD nano boundary-layer flows over stretching surfaces in a porous medium by rational Legendre collocation method

Solutions for the magnetohydrodynamic nano boundary layer fluid flow over a permeable stretching surface embedded in a porous medium are obtained numerically by rational Legendre collocation method. Two-dimensional and axisymmetric flows induced by stretching of the surface are considered. The effects of magnetic parameter, the porous parameter, first and second order slip and suction/injection parameters on the flow are discussed. A comparison of numerical results with previous published results is made and the results are found to be in good agreement.

An analytical solution of turbulent boundary layer fluid flow over a flat plate at high Reynolds number

Abstract This is an analytical investigation of turbulent boundary layer flow over a flat plate in the range of Reynolds number between 10 6 and 10 9 . With the use of novel similarity variables, the governing partial differential equations are transformed to an ordinary differential equation with inconsistent coefficients and they are solved analytically via the optimal homotopy analysis method (OHAM). To achieve the convergence of analytical series solutions, residual errors have been calculated and minimized. In addition, the distribution of the velocity profile, friction coefficient and thickness of the boundary layer are calculated and compared with the pertained experimental results in the literature, where good agreements between them are observed. Based on the series solution, analytical expressions for the friction coefficient and the hydrodynamic boundary layer thicknesses were proposed and compared with previously existed expressions. It was shown that the proposed expressions are highly accurate for the high Reynolds number.

Numerical solutions for a compressible dusty fluid flow along a vertical wavy cone

The purpose of this paper is to establish the detailed parametric study for compressible natural convection flow of two-phase dusty fluid along a vertical wavy cone. Typical sinusoidal surface is used to elucidate the heat transport phenomena for the compressible dusty fluid. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge is removed. The resulting equations are then solved straightforwardly by implicit finite difference method. The influence of compressibility, dusty fluid and the transverse curvature of the surface are discussed in detail in terms of local heat transfer rate, skin friction coefficient, velocity and temperature distributions. In order to ensure the accuracy, comparison with some special cases are also presented and the agreement is found to be very good. The key observation from the present study is that the half-cone angle, ϕ, and mass concentration parameter, Dρ, extensively promote the rate of heat transfer into the compressible boundary layer region.

Temperature and concentration stratification effects on non-Newtonian fluid flow past a cylindrical surface

The theme of present work is to report the numerical solution of mixed convection tangent hyperbolic fluid flow towards stretching cylindrical surface immersed in a double stratified media. The fluid flow is attained through no slip condition. The flow regime characteristics are modelled in terms of partial differential equations. A similarity transformation is used to transform partial differential equations into coupled non-linear ordinary differential equations. A computational algorithm is executed to predict numerical results. The effects of flow controlling parameters namely, mixed convection parameter, thermal stratification and solutal stratification parameters on velocity, temperature and concentration are examined and offered by means of graphical outcomes. It is noticed that in the presence of mixed convection effect both the fluid temperature and concentration are decreasing function of thermal stratification and solutal stratification parameters respectively. The obtained values are certified by developing comparison with existing values and an excellent agreement is observed which confirms the execution of computational algorithm.

Numerical Simulation of Turbulent Blood Flow in the System of Coronary Arteries with Stenosis

In this paper, we propose a mathematical model of turbulence flow of fluid through a deformable channel to study the pulsatile blood flow in the coronary system with arterial stenosis. Blood is assumed to be an incompressible non- Newtonian fluid and its motion is considered as turbulent and modelled by the mass and momentum conservations with turbulent mixing energy and specific dissipation rate. The mechanical deformation of the arterial wall is modelled by a hyperelastic differential equation. The pulsatile behaviour during each heartbeat is assigned on the entrance and exit boundaries. Numerical simulation based on the Finite Element method for the solution of arterial wall deformation, and the Arbitrary Lagrangian Eulerian Finite Volume method for the turbulence fluid-flow solution is used to investigate the effect of stenosis severity at the proximal part of the left anterior descending artery on the blood velocity, the pressure distribution and the wall shear stresses along the flow direction.

DRBEM solution of biomagnetic fluid flow and heat transfer in cavities-CMMSE2016

In this paper, we investigate the fully developed, laminar, forced convection flow of an electrically non-conducting, viscous, biomagnetic fluid in the 2D cross-section (cavity) of a long impermeable pipe. The fluid is under the influence of a point magnetic source placed below the cavity. The dual reciprocity boundary element method (DRBEM) with constant and linear elements is used for solving the governing equations resulting from the Navier–Stokes and energy equations together with magnetization and buoyancy forces. The fundamental solution of Laplace equation is made use of converting differential equations to boundary integral equations by taking all the terms other than Laplacian as inhomogeneity in the Poisson’s equations for the velocity components, pressure and the temperature of the fluid. The unknown pressure boundary conditions are approximated through momentum equations by using finite difference approximation for the pressure gradients and DRBEM coordinate matrix for the other terms. All the space derivatives are also calculated by DRBEM coordinate matrix which is one of the main advantages of DRBEM. Pipe axis velocity is also computed. The effects of magnetization and the buoyancy force on the fluid with or without viscous dissipation term in the energy equation are investigated in square and lid-driven cavities for several values of magnetic (Mn) and Rayleigh (Ra) numbers. It is observed that the flow and heat transfer are significantly affected with increasing values of Mn and Ra. DRBEM gives small sized linear systems due to its boundary only nature at a considerably low computational expense.

Transient experimental and modelling studies of laser-textured micro-grooved surfaces with a focus on piston-ring cylinder liner contacts

This paper presents a comparison between the results from numerical modelling and experiments to shed light on the mechanisms by which surface texture can reduce friction when applied to an automotive cylinder liner. In this configuration, textured features move relative to the piston-liner conjunction and to account for this our approach is to focus on the transient friction response to individual pockets as they pass through, and then leave, the sliding contact. The numerical approach is based on the averaged Reynolds’ equation with the Patir & Cheng's flow factors and the p-θ Elrod-Adams mass-conserving cavitation model. The contact pressures that arise from the asperity interactions are solved simultaneously to the fluid flow solution using the Greenwood and Tripp method. The experimental data is produced using a pin-on-disc set up, in which laser textured pockets have been applied to the disc specimen. Under certain conditions in the mixed and boundary lubrication regimes, both model and experimental results show i) an increase in friction as the pocket enters the contact, followed by ii) a sharp decrease as the pocket leaves the contact, and then iii) a gradual decay back to the pre-entrainment value. From the evidence obtained for the first time from the proposed combined modelling and experimental investigation conducted under carefully controlled conditions, we suggest that these three stages occur due to the following mechanisms: i) a reduction in fluid pressure due to the increased inlet gap, ii) inlet suction as the cavitated fluid within the pocket draws lubricant into the contact, and iii) film thickness decay as oil is squeezed out of the contact. The interplay of these three mechanisms is shown to control the response of micro-textured surfaces under all lubrication regimes.

Exact and approximate analytic solutions of the thin film flow of fourth-grade fluids by the modified Adomian decomposition method

Purpose The purpose of this paper is to first deduce a new form of the exact analytic solution of the well-known nonlinear second-order differential equation subject to a set of mixed nonlinear Robin and Neumann boundary conditions that model the thin film flows of fourth-grade fluids, and second to compare the approximate analytic solutions by the Adomian decomposition method (ADM) with the new exact analytic solution to validate its accuracy for parametric simulations of the thin film fluid flows, even for more complex models of non-Newtonian fluids in industrial applications. Design/methodology/approach The approach to calculating a new form of the exact analytic solution of thin film fluid flows rests upon a sequence of transformations including the modification of the classic technique due to Scipione del Ferro and Niccolò Fontana Tartaglia. Next the authors establish a lemma that justifies the new expression of the exact analytic solution for thin film fluid flows of fourth-grade fluids. Second, the authors apply a modification of the systematic ADM to quickly and easily calculate the sequence of analytic approximate solutions for this strongly nonlinear model of thin film flow of fourth-grade fluids. The ADM has been previously demonstrated to be eminently practical with widespread applicability to frontier problems arising in scientific and engineering applications. Herein, the authors seek to establish the relative merits of the ADM in the context of the thin film flows of fourth-grade fluids. Findings The ADM is shown to closely agree with the new expression of the exact analytic solution. The authors have calculated the error remainder functions and the maximal error remainder parameters in the error analysis to corroborate the solutions. The error analysis demonstrates the rapid rate of convergence and that we can approximate the exact solution as closely as we please; furthermore the rate of convergence is shown to be approximately exponential, and thus only a low-stage approximation will be adequate for engineering simulations as previously documented in the literature. Originality/value This paper presents an accurate work for solving thin film flows of fourth-grade fluids. The authors have compared the approximate analytic solutions by the ADM with the new expression of the exact analytic solution for this strongly nonlinear model. The authors commend this technique for more complex thin film fluid flow models.

Analytical Stability Analogue for a Single-Phase Natural-Circulation Loop

Numerical solutions for transient fluid flow in nuclear systems often suffer from the effects of numerical diffusion and damping making the assessment of system stability rather difficult. Efforts for coping with this problem include research and development of algorithms with improved fidelity for stability calculations as they apply to particular problems. Benchmarking exercises in comparison with specially designed experiments are necessary to verify algorithmic fidelity and guide the development and adjustments of the algorithms. In this paper, an analytical approach is introduced where a simple model—an analogue—is constructed such that the basic instability mechanisms are represented in a form that lends itself to analytical solutions that are free from the diffusion and damping problems that plague finite volume algorithms. Direct conclusions can be made regarding the stability of a system in the case where the analogue closely resembles the system under study. However, when the system is too complex for direct assessment, the stability fidelity of numerical solutions can be assessed by comparing the numerical solution for the simple system with the analytical solution and using the comparison to quantify any damping effects and justify the application of the numerical method to the complex representation of the real system under study. The theoretical analysis is supported by reference to recent test data in the NuScale Integral System Test (NIST) facility representing a scaled-down NuScale module.

Two-phase dusty fluid flow along a cone with variable properties

In this paper numerical solutions of a two-phase natural convection dusty fluid flow are presented. The two-phase particulate suspension is investigated along a vertical cone by keeping variable viscosity and thermal conductivity of the carrier phase. Comprehensive flow formations of the gas and particle phases are given with the aim to predict the behavior of heat transport across the heated cone. The influence of (1) air with particles, (2) water with particles and (3) oil with particles are shown on shear stress coefficient and heat transfer coefficient. It is recorded that sufficient increment in heat transport rate can be achieved by loading the dust particles in the air. Further, distribution of velocity and temperature of both the carrier phase and the particle phase are shown graphically for the pure fluid (air, water) as well as for the fluid with particles (air-metal and water-metal particle mixture).

Electro-osmotic and pressure-driven flow of viscoelastic fluids in microchannels: Analytical and semi-analytical solutions

In this work, we present a series of solutions for combined electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels. The solutions are semi-analytical, a feature made possible by the use of the Debye–Hückel approximation for the electrokinetic fields, thus restricted to cases with small electric double-layers, in which the distance between the microfluidic device walls is at least one order of magnitude larger than the electric double-layer thickness. To describe the complex fluid rheology, several viscoelastic differential constitutive models were used, namely, the simplified Phan-Thien–Tanner model with linear, quadratic or exponential kernel for the stress coefficient function, the Johnson-Segalman model, and the Giesekus model. The results obtained illustrate the effects of the Weissenberg number, the Johnson-Segalman slip parameter, the Giesekus mobility parameter, and the relative strengths of the electro-osmotic and pressure gradient-driven forcings on the dynamics of these viscoelastic flows.

Non-similarity Solution of Micropolar Fluid Flow over a Truncated Cone with Soret and Viscous Dissipation Effects Using Spectral Quasilinearization Method

This paper is an investigation of viscous dissipation and Soret effects on laminar natural convection flow over a truncated cone immersed in a micropolar fluid with convective boundary condition. For this complex fluid flow problem, the similarity solution does not exist and hence the non-similarity transformations are used to convert the governing fluid flow equations along with associated boundary conditions into a set of non-dimensional form. Due to several advantages of spectral methods over the finite difference and finite element methods, the spectral quasi-linearization method is employed to solve the system of non-similar, coupled, partial differential equations. The numerical results point out that, in the presence and absence of Soret number, the Nusselt number, wall couple stress and Sherwood number decrease, but the temperature, concentration and skin friction increase with an increase of coupling parameter. As the Boit number enhances, the skin friction, Nusselt number and Sherwood number enhance but the wall couple stress reduces in the presence of viscous dissipation parameter.

Thermal diffusion and chemical reaction effects on unsteady flow past a vertical porous plate with heat source dependent in slip flow regime

The present study investigates an analytical solution of free convective unsteady fluid flow in presence of thermal diffusion and chemical reaction effects past a vertical porous plate with heat source dependent in slip flow regime. The plate is assumed to move with a constant velocity in the direction of fluid flow, while free stream velocity is assumed to follow exponentially increasing small perturbation law. The velocity, temperature and concentration profiles are presented graphically for different values of the parameters entering into the problem. Finally the effects of pertinent parameters on the skin friction coefficient, Nusselt number and Sherwood numbers distributions are derived and have shown through graphs and tables by using perturbation technique.

Numerical analysis of the solutions for 1d compressible viscous micropolar fluid flow with different boundary conditions

The intention of this work is to concern the numerical solutions to the model of the nonstationary 1d micropolar compressible viscous and heat conducting fluid flow that is in the thermodynamical sense perfect and polytropic. The mathematical model consists of four partial differential equations, transformed from the Eulerian to the Lagrangian description, and which are associated with different boundary conditions. By using the finite difference scheme and the Faedo–Galerkin method we make different numerical simulations to the results of our problems. The properties of both numerical schemes are analyzed and numerical results are compared on the chosen test examples. The comparison of the numerical results on problems that have the homogeneous or the non-homogeneous boundary conditions for velocity and microrotation show good agreement of both approaches. However, the advantage of the used finite difference method over the Faedo–Galerkin method lies in the simple implementation of the non-homogeneous boundary conditions and in the possibility of approximation of the free boundary problem on which the Faedo–Galerkin method is not applicable.

Assumptions of the analytical solution for solute transport in a fracture–matrix system

This study focuses on numerical modeling of fluid flow and solute transport in rough-walled rock fractures and fracture-matrix systems, with the main aim to investigate the impacts of fracture surface roughness on flow and transport processes in rock fractures. Both 2D and 3D fracture models were built from laser-scanned surface tomography of a real granite rock sample, to consider realistic features of surface tomography and potential asperity contacts. The flow was simulated by directly solving the Navier-Stokes equations (NSE) and the transport was modeled by solving the advection-dispersion equation (ADE) in the entire domain of fracture-matrix system, including matrix diffusion process. Such direct simulations provided detailed flow and concentration fields for quantitatively analysis of flow and transport behavior. The detailed analysis of surface roughness decomposition, complex flow patterns (i.e., channeling, transverse and eddy flows), effective advective flow apertures, effective transmissivity, effective dispersivity, residence time, transport resistance and specific surface area demonstrated significant impacts of realistic fracture surface roughness on fluid flow and solute transport processes in rock fractures. The results show that the surface roughness and shear displacement caused asperity contacts significantly enhance nonlinearity and complexity of flow and transport processes in rough-walled fractures and fracture-matrix systems. The surface roughness also causes invasion flows in intersected fractures which enhance solute mixing at fracture intersections. Therefore, the fracture surface roughness is an important source of uncertainty in application of such simplified models like cubic law (CL) for fluid flow and analytical solutions for solute transport in rock fractures. The research conducted advances our understanding of realistic flow and transport processes in natural fractured rocks. The results are useful for model validation/extension, uncertainty analysis/quantification and laboratory experiments design in the context of various applications related to fracture flow and transport.

Challenges and Remedies in Interdisciplinary PG Programme

The world currently is reeling under acute shortage in essential resources for human existence due to growing population and elevated living standards. Today society at large demands more contributions from engineering community in terms of devising better and cost effective solutions to address existing problems. The engineering practice hence demands better skill sets that are honed to meet present day societal expectations. This situation demands improved teaching-learning methods that prepares engineering graduates to operate in multidisciplinary teams to accomplish the targeted solution or goal. The present work showcases implementation of effective pedagogical approach in Computational fluid dynamics (CFD) laboratory course prescribed for interdisciplinary PG Programme in Energy Systems Engineering. The course intends to enable students in usage of computational tools that includes commercial and open source software packages for fluid flow analysis. The CFDcourse has application in diverse engineering domains as a precursor for selection and optimization of functional elements in products that involve fluid flows.The course delivery posed several challenges due to diversity within student group and need of mathematical proficiency. The exercises designed in CFD lab-course related to execution of complete cycle of analysis taking into account formulation and solution of fluid flow and heat transfer aspects. The course thereby related to attainment of Programme outcomes (POs) covering areas of Research capabilities, Competence on use of modern computational tools, Multi-disciplinary team activity and communication aspects. The results obtained provide useful inputs to develop measures that will improve the delivery of the course for next batch of students opting the course.

Viscoelastic fluid flow in a prismatic channel of square cross-section with reference to the example of rubber mixtures

Flow in a prismatic channel of the melts of the SKI-3 and SKMS30-ARKM-15-based rubber mixtures widely used in the chemical industry is numerically investigated. The description of these media, which exhibit viscoelstic properties when being processed, requires a particular approach that would take their rheological behavior and various anomalies into account. Amidst many rheological equations governing flows of rheologically complex media the equation that would ensure not only the good reliability of the results but also the feasibility in its practical use should be selected. The special features of viscoelastic fluids clearly manifest themselves in the flow in a prismatic channel of a noncircular cross-section. Secondary flows characteristic of the viscoelastic flows in such channels force the fluid particles to move in spiral trajectories along the channel. In the numerical calculations the Phan-Thien–Tanner (PTT) rheological model is used; its parameters are obtained on the basis of experimental data. The calculations are performed using the COSMOL Multiphysics software complex. the method of solution was tested against the analytical solution of the PTT fluid flow in a round tube which was compared with the numerical solution.

Perturbation solutions for a micropolar fluid flow in a semi-infinite expanding or contracting pipe with large injection or suction through porous wall

Abstract We investigate an unsteady incompressible laminar micropolar flow in a semi-infinite porous pipe with large injection or suction through a deforming pipe wall. Using suitable similarity transformations, the governing partial differential are transformed into a coupled nonlinear singular boundary value problem. For large injection, the asymptotic solutions are constructed using the Lighthill method, which eliminates singularity of solution in the high order derivative. For large suction, a series expansion matching method is used. Analytical solutions are validated against the numerical solutions obtained by Bvp4c.