Unsteady Flow Problems Research Articles

Natural Convective Effects on MHD Boundary Layer Nanofluid Flow over an Exponentially Accelerating Vertical Plate

The problem of unsteady natural convective nanofluid flow along with an exponentially accelerating vertical plate under the influence of transverse magnetic field is discussed in two important cases when the magnetic lines of force are fixed relative to the fluid or the moving plate. The governing equations are transformed into dimensionless form and tackled with the usual time-frequency Laplace transform technique. The impacts of various parameters on the heat transfer characteristics and nanofluid flow transport with thermal radiation, heat generation/absorption, and nanoparticle volume concentration have been studied through graphs.

Mass Transfer Effect on a Rotating MHD Transient Flow of Liquid Lead Through a Porous Medium in Presence of Hall and Ion Slip Current with Radiation

A problem of unsteady MHD convective flow of liquid lead through an impulsively started semi infinite vertical porous plate in presence of a transversely applied uniform magnetic field under the effects of Hall current, ion slip current and chemical reaction is investigated. The fluid is considered to be incompressible while the magnetic Reynolds number is assumed to be very small. An exact solution to the flow model is obtained adopting Laplace Transform Technique in closed form. The effects of the relevant physical parameters on the velocity field, temperature field and concentration field are displayed graphically and the effects on skin friction, Nusselt number and Sherwood number are presented in tabular form.

Improved simplified and highly stable lattice Boltzmann methods for incompressible flows

In this work, improved simplified and highly stable lattice Boltzmann methods (SHSLBMs) are developed for incompressible flows. The SHSLBM is a newly developed scheme within the lattice Boltzmann method (LBM) framework, which utilizes the fractional step technology to resolve the governing equations recovered from lattice Boltzmann equation (LBE) and reconstructs the equations in the Lattice Boltzmann frame. By this treatment, the SHSLBM directly tracks the macroscopic variables in the evolution process rather than the distribution functions of each grid node, which greatly saves virtual memories and simplifies the implementation of physical boundary conditions. However, the Chapman–Enskog expansion analysis reveals that the SHSLBM recover the weakly compressible Navier–Stokes equations with the low Mach number assumption. Therefore, the original SHSLBM can be regarded as an artificial compressible method and may cause some undesired errors. By modifying the evolution equation for the density distribution function, the improved SHSLBMs can eliminate the compressible effects. The incompressible SHSLBMs are compared with the original SHSLBM in terms of accuracy and stability by simulating several two-dimensional steady and unsteady incompressible flow problems, and the results demonstrate that the present SHSLBMs ensure the second order of accuracy and can reduce the compressible effects efficiently, especially for the incompressible flows with large pressure gradients. We then extended the present SHSLBMs to study the more complicated two-dimensional lid-driven flow and found that the present results are in good agreement with available benchmark results.

Time-domain TEBEM method for mean drift force and moment of ships with forward speed under the oblique seas

A numerical method for solving 3D unsteady potential flow problem of ship advancing in waves is put forward. The flow field is divided into an inner and an outer domain by introducing an artificial matching surface. The inner domain is surrounded by ship wetted surface and matching surface as well as part of the free surface. The free surface condition for the inner domain is formulated by perturbation about the double-body flow or uniform incoming flow assumption. The outer domain is surrounded by matching surface and the rest free surface as well as infinite far-field radiation boundary. The free surface condition for the outer domain is formulated by perturbation about uniform incoming flow. The simple Green function and transient free surface Green function are used to form the boundary integral equation (BIE) for the inner and outer domains, respectively. Taylor Expansion Boundary Element Method (TEBEM) is utilized to solve the double-body flow and inner domain and outer domain unsteady flow BIE. Matching conditions for the inner domain flow and outer domain flow are enforced by the continuity of velocity potential and normal velocity on the matching surface. Direct pressure integration on ship wetted surface is used to obtain the first-order and second-order wave forces (moments). The numerical predictions on the displacement, added resistance, sway mean drift force and yaw mean drift moment of the modified KVLCC2 ship at different forward speeds are investigated by the proposed TEBEM method. It is also compared with the other numerical results. The physical tank experiment results are also developed to validate the accuracy of numerical tank results. Compared with the experiment solutions, a good agreement can be obtained by TEBEM method.

On the existence and uniqueness of solution for squeezing nanofluid flow problem and Green–Picard’s iteration

PurposeThis study aims to explore the idea of solving the problem of squeezing nanofluid flow between two parallel plates using a novel mathematical method.Design/methodology/approachThe unsteady squeezing flow is a coupled fourth-order boundary value problem with flow velocity and temperature as the desired unknowns. In the first step, the conditions that guarantee the existence of a unique solution are obtained. Then following Green’s function-based approach, an iterative method for solving the problem is developed.FindingsThe accuracy of the method is examined by comparing the obtained results with existing numerical data, indicating excellent agreement between the two. In addition, the effects of nanoparticle shape and volume fraction on the flow and heat transfer characteristics are addressed. The results reveal that although the nanoparticle shape strongly affects the temperature distribution in the squeezing flow, it only has a slight impact on the velocity field. Furthermore, the highest and lowest Nusselt numbers belong to the platelets and spherical nanoparticles, respectively.Originality/valueA semi-analytical method with computational support is developed for solving the unsteady squeezing flow problem. Moreover, the existence and uniqueness of the solution are discussed for the first time.

Unsteady aerodynamic characteristics of slender body at extra-wide angle-of-attack range

For complicated unsteady separated flow problem of slender body at extra-wide of angle of attack range, delayed detached eddy simulation based on shear stress transport turbulence model is adopted to simulate the unsteady flows of slender body numerically in Mach number 0.6 and at the angle of attack of 0° to 180°. The calculated results of unsteady aerodynamic forces and the fluctuating pressure are analyzed which have a good agreement with experimental results. The unsteady amplitude of the lateral force is particularly strong at the angle of attack of 45 to 165°. The Strouhal number of lateral force range from 0.177 to 0.31. The investigation of unsteady vortical flow characteristics indicate the dominant frequency characteristic of aerodynamic force is mainly generated by Karman-vortex-street-like flow induced by the cylindrical body and no obvious dominant frequency is found in the massively separation past the canard surface.

Unsteady Boundary Layer Flow of a Micropolar Fluid at a Two-Dimensional Stagnation Point on a Moving Wall

The problem of unsteady boundary layer flow of a micropolar fluid at a two-dimensional stagnation point on a moving wall when the free stream velocity and wall temperature vary arbitrarily with time has been studied. The governing partial differential equations were solved numerically by the Keller box method. The micropolar fluid flow model on a moving wall is capable of predicting the results which exhibit turbulent flow characteristics. Numerical results obtained for velocity, micro rotations and temperature distributions are shown graphically. The velocity distribution has been illustrated for several positive and negative values of the wall velocity. The skin friction, couple stress and transfer rate are found to be strongly dependent on the coupling parameter and time, however the effect of variation in the micro rotation parameter is visible appreciably in case of couple stress only.

Estimation of Parameters for Non-Equilibrium Phase Transitions during the Flow of Oil and Gas Mixtures

Problems of unsteady gas-liquid flows in wellbores with phase transitions are common for hydrocarbon production and well drilling. Typically, flow in wellbores is sufficiently fast which requires taking into account the non-equilibrium nature of phase transitions. The set of equations describing conservation of mass for components and momentum conservation for the mixture is supplemented by the relaxation equation for concentration of gas dissolved in the liquid. It is known that the characteristic times of gas evolution from the liquid and gas dissolution in the liquid differ significantly and depend on fluid properties, thermobaric conditions, and the flow pattern. Therefore, obtaining estimates of relaxation times for real flows turns to be a difficult problem. In this study, we propose a method for estimating the characteristic relaxation times for gas evolution and dissolution during the gas-liquid flow in a well. The method combines the solution of the convective diffusion equation for the growth/collapse of a vapor bubble in a liquid with the current parameters of the gas-liquid flow. Estimates of the relaxation times for the bubbly flow (small bubbles, gas evolution predominates) and slug flow (large bubbles, dissolution predominates), as functions of time from the beginning of the process, are obtained for the parameters of a real flow in a wellbore. It is shown that the obtained dependencies are consistent with the typical scaling of the diffusion process with respect to the size of bubbles. The results are important for mathematical simulation of gas-liquid flows in wellbores during hydrocarbon production, as well as for calculation of the gas-kick process during well drilling with oil-based muds.

Assessment of unsteady flow predictions using hybrid deep learning based reduced-order models

In this paper, we present two deep learning-based hybrid data-driven reduced-order models for prediction of unsteady fluid flows. These hybrid models rely on recurrent neural networks (RNNs) to evolve low-dimensional states of unsteady fluid flow. The first model projects the high-fidelity time series data from a finite element Navier–Stokes solver to a low-dimensional subspace via proper orthogonal decomposition (POD). The time-dependent coefficients in the POD subspace are propagated by the recurrent net (closed-loop encoder–decoder updates) and mapped to a high-dimensional state via the mean flow field and the POD basis vectors. This model is referred to as POD-RNN. The second model, referred to as the convolution recurrent autoencoder network (CRAN), employs convolutional neural networks (instead of POD) as layers of linear kernels with nonlinear activations, to extract low-dimensional features from flow field snapshots. The flattened features are advanced using a recurrent (closed-loop manner) net and up-sampled (transpose convoluted) gradually to high-dimensional snapshots. Two benchmark problems of the flow past a cylinder and the flow past side-by-side cylinders are selected as the unsteady flow problems to assess the efficacy of these models. For the problem of the flow past a single cylinder, the performance of both the models is satisfactory and the CRAN model is found to be overkill. However, the CRAN model completely outperforms the POD-RNN model for a more complicated problem of the flow past side-by-side cylinders involving the complex effects of vortex-to-vortex and gap flow interactions. Owing to the scalability of the CRAN model, we introduce an observer-corrector method for calculation of integrated pressure force coefficients on the fluid–solid boundary on a reference grid. This reference grid, typically a structured and uniform grid, is used to interpolate scattered high-dimensional field data as snapshot images. These input images are convenient in training the CRAN model, which motivates us to further explore the application of the CRAN-based models for prediction of fluid flows.

Reduced-order modelling of parameterised incompressible and compressible unsteady flow problems using deep neural networks

A non-intrusive reduced-order model for nonlinear parametric flow problems is developed. It is based on extracting a reduced-order basis from full-order snapshots via proper orthogonal decomposition and using both deep and shallow neural network architectures to learn the reduced-order coefficients variation in time and over the parameter space. Even though the focus of the paper lies in developing a reduced-order methodology for approximating fluid flow problems, the methodology is generic and can be used for the order reduction of arbitrary time-dependent parametric systems. Since it is non-intrusive, it is independent of the full-order computational method and can be used together with black-box commercial solvers. An adaptive sampling strategy is proposed to increase the quality of the neural network predictions while minimising the required number of parameter samples. Numerical studies are presented for two canonical test cases, namely unsteady incompressible laminar flow around a circular cylinder and transonic inviscid flow around a pitching NACA 0012 aerofoil. Results show that the proposed methodology can be used as a predictive tool for unsteady parameter-dependent flow problems.

Reduced-order modelling of parameterised incompressible and compressible unsteady flow problems using deep neural networks

Reduced-order modelling of parameterised incompressible and compressible unsteady flow problems using deep neural networks

Parameterized nonintrusive reduced‐order model for general unsteady flow problems using artificial neural networks

AbstractA nonintrusive reduced‐order model for nonlinear parametric flow problems is developed. It is based on extracting a reduced‐order basis from high‐order snapshots via proper orthogonal decomposition and using multilayered feedforward artificial neural networks to approximate the reduced‐order coefficients. The model is a generic and efficient approach for the reduction of time‐dependent parametric systems, including those described by partial differential equations. Since it is nonintrusive, it is independent of the high‐order computational method and can be used together with black‐box solvers. Numerical studies are presented for steady‐state isentropic nozzle flow with geometric parameterization and unsteady parameterized viscous Burgers equation. An adaptive sampling strategy is proposed to increase the quality of the neural network approximation while minimizing the required number of parameter samples and, as a direct consequence, the number of high‐order snapshots and the size of the network training set. Results confirm the accuracy of the nonintrusive approach as well as the speed‐up achieved compared with intrusive hyper‐reduced‐order approaches.

Foundations for high-order, conservative cut-cell methods: Stable discretizations on degenerate meshes

Cut-cell methods for unsteady flow problems can greatly simplify the grid generation process and allow for high-fidelity simulations on complex geometries. However, cut-cell methods have been limited to low orders of accuracy. This is driven, largely, by the variety of procedures typically introduced to evaluate derivatives in a stable manner near the highly irregular embedded geometry. In the present work, a completely new approach, termed TEMO (truncation error matching and optimization), is taken to solve this problem. The approach is based on two simple and intuitive design principles. These principles directly allow for the construction of stable 8th order approximations to elliptic and parabolic problems. In addition, when combined with the non-linear optimization process of Ref. [6], these principles allow for stable and conservative 4th order approximations to hyperbolic problems without the addition of numerical dissipation. To the best of the authors' knowledge, these are the highest orders ever achieved for a cut-cell discretization by a significant margin. This is done for both explicit and compact finite differences and is accomplished without any geometric transformations or artificial stabilization procedures.

A basis for flow modelling

Abstract

Numerical simulation of unsteady flow of a viscous incompressible liquid in flat channels of arbitrary shape of heat exchangers

Reasonable development and creation of any device in which there is an interaction between the fluid flow and the elements of the flow parts (for example, heat exchangers, transport and power machines, main pipelines), is impossible without detailed information about the characteristics of the flow, about the forces on the surfaces that are around, about vibroacoustic phenomena, etc. Among the various methods of obtaining information about the characteristics of the flow, about the forces on surfaces that are flown around, about vibroacoustic phenomena, an important role is played by theoretical methods that rely on the equation of hydrodynamics and numerous ways to solve them. In this case, the main efforts are aimed at solving the system of Navier-Stokes equations. In this paper, a general method is described for the numerical solution of the problem of unsteady flow of a viscous incompressible fluid in flat channels of an arbitrary shape of heat exchangers. An effective solution to the problem is achieved by using adaptive networks. The mathematical model of the flow is based on the two-dimensional Navier-Stokes equations in the variables "flow function - vortex" and the Poissonequation for pressure, which are solved on the basis of the finite-difference method. A numerical simulation of the fluid flow in a flat curvilinear elbow is carried out at the Reynolds number Re = 1000. This form reflects the most characteristic features of the flow paths of various hydraulic machines, heat exchangers, hydraulic and pipeline systems. The presentation of the numerical results was carried out on the basis of the VISSIM graphic processing package. One of the main problems (difficulties) in the numerical solution of problems of mathematical physics is the representation of boundary conditions for regions of arbitrary shape. The implementation of various artificial methods that are now used in the approximation of both the curvilinear boundaries themselves and the boundary conditions on them can lead to significant losses in the accuracy of the solution. This is especially evident in problems in which solutions in the boundary region have maximum gradients. An effective method for solving this problem is the use of adapted grids for the computational domain. The essence of this method lies in the fact that such a coordinate system, not necessarily orthogonal, is found in which the boundary lines (surfaces) of the region coincide with the coordinate lines (surfaces). In the flat case, the computational domain is transformed into a rectangular one, and the limit curve is displayed on the sides of the rectangle. In practice, the problem of constructing an adapted mesh is reduced to finding functions that describe the mappings of the canonical (rectangular) region onto the region for which the problem was originally formulated, that is, for the two-dimensional case, the functions x (ξ, η), y (ξ, η) are determined.

A self-similar solution for transient flow in a pipeline

In this study, we examine the classical problem of unsteady fluid flow in a long pipeline, induced by reduction/growth in the fluid head. This problem was solved by using the symmetry properties of the water hammer equations, which enable us to transform the time and the space coordinates into one independent coordinate. In other words, the two partial differential equations which are characterized by the unsteady flow in a long pipeline were reduced to one nonlinear ordinary differential equation.In general, self-similar solutions are an effective tool for describing transient phenomena in various flow fields, where the problem lacks a characteristic length or time scale. The development of self-similar solutions simplifies the physical problem and changes the partial non-linear differential equations to the level of ordinary differential equations. As a result, a closed form analytical solution for the governing equations (continuity and momentum) is derived for several transient situations. Based on data of heads, collected from the pipeline for transient situations, the model was calibrated and its applicability to predict head distribution in the pipeline has been shown.

Unsteady stagnation-point boundary layer flows of power-law fluids over a porous flat plate

The problem of unsteady stagnation-point flows of power-law fluids over a porous flat plate with mass transfer is considered with a view to examine the rheological behaviors of the fluids. This study is completely based on the four physical parameters, namely, flow strength parameter a, mass transfer parameter d, unsteadiness parameter $$\beta$$ and non-Newtonian power-law index n. For $$d=0$$ , the numerical results of this analysis reveal the existence of two types of solutions - one is attached flow solution (AFS) and the other is reverse flow solution (RFS) in a definite range of n ( $$0< n \le 2$$ ) when (a, $$\beta )= (1, - 1)$$ . The present analysis confirms that the velocity profile for any dilatant fluid $$(n > 1)$$ matches smoothly with the free stream velocity for a suitable amount of blowing $$d(< 0)$$ depending upon the values of n. We will also discuss the asymptotic behaviors of the boundary layer flows for large values of d, i.e., for $$d \rightarrow \pm \infty$$ . The asymptotic analysis ensures the existence of the above two solutions for large values of suction $$d>0$$ , whereas the boundary layer solution is terminated after a certain value of blowing $$d<0$$ , dependent on the values of $$\beta (< 0)$$ and n. Below this critical value of blowing d, this unsteady flow problem also provides us with a solution which does not appear to have a boundary layer character.

Permanent solutions for some oscillatory motions of fluids with power-law dependence of viscosity on the pressure and shear stress on the boundary

Abstract In this paper, we provide simple expressions for the permanent solutions corresponding to some oscillatory motions of two classes of Newtonian fluids with power-law dependence of viscosity on the pressure between two infinite horizontal parallel plates. The fluid motion is generated by the lower plate that applies an oscillatory shear stress to the fluid. Such solutions, which are lack in the existing literature, can be useful both for those who want to eliminate the transients from their experiments and as tests to verify numerical schemes that are developed to study complex unsteady flow problems of these fluids. The similar solutions corresponding to the motion due to a constant shear stress on the boundary are also determined and, contrary to our expectations, the shear stresses are constant on the whole flow domain although the associated velocity fields depend both of the spatial variable and the dimensionless pressure-viscosity coefficient. Finally, for validation, some comparative graphical illustrations are included and the convergence of starting solutions to the permanent solutions is graphically proved. Spatial profiles of starting solutions are also provided.

Evaluation of a nonlinear variational multiscale method for fluid transport problems

Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems. VMS methods avoid the assumption of separable nonlinearity and the reliance on empirical small-scale models by using a variational decomposition of scales together with a residual-based approximation of the small-scales. Evaluation of a nonlinear VMS approach, denoted as VMSn, is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems arising from fluid flow models. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMSn treats the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. The VMSn approach is complemented with two algebraic approximations of the small-scales: one based on the main diagonal of the transport matrices and another that preserves transport fluxes and is suitable for generic TADR systems. The suitability of the VMSn approach for handling general TADR problems and regimes is evaluated with benchmark incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, the turbulent free jet, and the two-temperature arc in crossflow. Simulation results show that VMSn leads to minor improvements in accuracy with respect to the classical VMS for the laminar flow problems, but to significantly greater accuracy for the turbulent flows and the unsteady plasma flow problems, while using the same cohesive numerical formulation.

Unsteady problem of magnetohydrodynamic heat plus mass transfer convective flow over a moveable plate with effects of thermophoresis and thermal radiation

AbstractThis paper investigates the problem of unsteady magnetohydrodynamic heat plus mass transfer convective flow over a moveable vertical plate with the influence of thermophoresis and thermal radiation. The physical problem is governed by a set of partial differential equations. These sets of equations are coupled and are nonlinear. They were transformed into a dimensionless form of equations by introducing appropriate nondimensional quantities. An iterative method called the spectral relaxation method was used to linearize and decouple the set of dimensionless equations. Results were presented both in graphs and tables. It was found out that thermophoresis parameter has a significant effect on velocity and concentration fields. The thermal radiation is seen to have a significant effect on velocity and temperature fields. The skin friction is seen to increase the moment thermal Grashof number is increased. The model of Newtonian fluid flow over a moveable vertical plate is considered. The plate was considered moving toward the ‐direction and the radiative heat flux is only with respect to . This study considered effects of viscous dissipation, thermophoresis, and radiation on heat plus mass transfer. This, to the best of our knowledge, has not been considered in the literature.