Unsteady Flow Problems Research Articles

Numerical Analysis and Experimental Validation of Trimaran and Pentamaran Resistance at Various Separation Distances

Trimaran and pentamaran are multihull types with an odd number of hulls, namely three and five hulls, generally consisting of one center hull and two or four side hulls smaller than the center hull, which can reduce ship resistance. The trimaran and pentamaran have a more complex phenomenon than the monohull, because of the interaction between the main hull and the side hull, which causes interference caused by changes in flow velocity, pressure changes, and wave interactions generated by each hull. The objective of this study is to analyze the resistance of trimaran and pentamaran NPL-4b models with transom-symmetrical hull and separation distances, specifically S/L ratios of 0.2, 0.3, and 0.4. Since a more limited base of experience exists for multihull ships, experimental or numerical modeling techniques are essential for designers. Numeric investigations were conducted using Numeca software, and experiments were performed in a towing tank. Both methods follow ITTC procedures. Furthermore, the numerical analysis with CFD simulation modifies the Navier-Stokes equation using the turbulence model k-ꞷ SST to generate the RANS equation so that unsteady fluid flow problems can be calculated. It can be implemented in predicting resistance in Froude numbers (Fr) 0.2 to 0.6 at the systematic series of trimaran and pentamaran hull shapes at the model scale. The simulation results were compared to experimental data to validate the resistance of the ships. Overall, good resistance was produced by the trimaran and pentamaran in the C configuration at an S/L ratio of 0.4 with a total resistance coefficient CT of 6.60 x 10-3 and 7.37 x 10-3, respectively. The two results are in good agreement, both methods have a discrepancy of 3.70 %. Fluctuations influence the resistance in the wetted surface area (WSA), wave interactions between hulls, ship velocity, and wave propagation in the aft hull.

Mathematical Analysis of a Navier–Stokes Model with a Mittag–Leffler Kernel

In this paper, we establish the existence and uniqueness results of the fractional Navier–Stokes (N-S) evolution equation using the Banach fixed-point theorem, where the fractional order β is in the form of the Atangana–Baleanu–Caputo fractional order. The iterative method combined with the Laplace transform and Sumudu transform is employed to find the exact and approximate solutions of the fractional Navier–Stokes equation of a one-dimensional problem of unsteady flow of a viscous fluid in a tube. In the domains of science and engineering, these methods work well for solving a wide range of linear and nonlinear fractional partial differential equations and provide numerical solutions in terms of power series, with terms that are simple to compute and that quickly converge to the exact solution. After obtaining the solutions using these methods, we use Mathematica software Version 13.0.1.0 to present them graphically. We create two- and three-dimensional plots of the obtained solutions at various values of β and manipulate other variables to visualize and model relationships between the variables. We observe that as the fractional order β becomes closer to the integer order 1, the solutions approach the exact solution. Lastly, we plot a 2D graph of the first-, second-, third-, and fourth-term approximations of the series solution and observe from the graph that as the number of iterations increases, the approximate solutions become close to the series solution of the fourth-term approximation.

Exact exploration of time fractional-based magnetized flow of a generalized second grade fluid through an oscillating rectangular duct

To model several engineering and physical models, the approach of the fractional derivative is highly anticipated. As compared to the ordinary derivatives, the fractional derivatives with more flexibility can estimate the data due to the involvement of the fractional-order derivatives. Due to these advantages of the fractional approach, this study communicates with the determination of the fractional-based exact outcomes of an oscillatory rectangular duct problem of a generalized second-grade fluid. The approach of the fractional operator is involved in the relationship of the constitutive equations. For cosine oscillation of the rectangular duct, exact results of the magnetized unsteady flow problem are evaluated through the technique of Laplace transform with double finite Fourier sine transform. This study concludes that the velocity field exhibits escalating behavior relative to the improved fractional parameter. Moreover, the magnetic parameter with increasing values declines the flow field while the accelerating values of the fluid parameter enhance the velocity field.

Two Models on the Unsteady Heat and Fluid Flow Induced by Stretching or Shrinking Sheets and Novel Time-Dependent Solutions

Abstract This study sheds light on unsteady heat and fluid flow problems over stretching and shrinking surfaces, enriching our understanding of these complex phenomena. We derive two mathematical models using a rigorous approach. The first model aligns with the model commonly employed by researchers in this field, but its steady-state solution remains trivial. The second model, introduced in this work, demonstrably captures the physically relevant steady-state solutions well-studied in the literature. Notably, we introduce new similarity solutions for the temperature field specifically within the first model. We further demonstrate that a uniform wall temperature condition leads to the optimal heat transfer rate. While similarity solutions can be derived for specific cases with the second model, nonsimilar solutions may be necessary for more general scenarios. We discuss the implications of our analysis for stagnation-point flow and non-Newtonian viscoelastic fluid flow problems, illuminating future research directions in the open literature.

Kinetic and thermodynamic approach to precisely solve the unsteady Rayleigh flow problem of a rarefied homogeneous charged gas under external force influence

Abstract An extension and further development of our previous article [J. Non-equilibrium Thermodyne. 37 (2012), 119–141] is presented. We study the irreversible non-equilibrium thermodynamics (INT) properties of the exact solution to the dilute homogeneously charged gas problem with unsteady Rayleigh flow. In contrast to previous research, the charged gas flows under the influence of an external force, the flat plate oscillates, and the displacement current term is considered, leading to significant advancements in understanding natural plasma dynamics. We are solving the Boltzmann kinetic equation (BKE) Krook model supplemented by Maxwell’s equations. We used a travelling wave and moments method with an electron velocity distribution function (EVDF). To the best of our knowledge, as three new scientific achievements, we introduced a new mathematical model for calculating the thermodynamic forces, kinetic coefficients, and fluxes variables, Equations (28–40) and (50–54). Second, we determined, with reasonable accuracy, the thermodynamic equilibrium time of electrons, t equ = 26.7955, under an external force. We clarify the difference between equilibrium EVDF and perturbed EVDF and take advantage of BKE to account for non-equilibrium thermodynamic principles. For diamagnetic and paramagnetic plasmas, the extended Gibbs equation predicts ratios between various contributions to the internal energy change (IEC) is presented. A standard laboratory argon plasma model is used to apply the results.

A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity

A fractional-step method is proposed and analyzed for solving the incompressible thermal Navier–Stokes equations coupled to the convection–conduction equation for heat transfer with a generalized source term for which the viscosity and thermal conductivity are temperature-dependent under the Boussinesq assumption. The proposed method consists of four steps all based on a viscosity-splitting algorithm where the convection and diffusion terms of both velocity and temperature solutions are separated while a viscosity term is kept in the correction step at all times. This procedure preserves the original boundary conditions on the corrected velocity and it removes any pressure inconsistencies. As a main feature, our method allows the temperature to be transported by a non-divergence-free velocity, in which case we show how to handle the subtle temperature convection term in the error analysis and establish full first-order error estimates for the velocity and the temperature solutions and 1/2-order estimates for the pressure solution in their appropriate norms. The theoretical results are examined by an accuracy test example with known analytical solution and using a benchmark problem of Rayleigh–Bénard convection with temperature-dependent viscosity and thermal conductivity. We also apply the method for solving a problem of unsteady flow over a heated airfoil. The obtained results demonstrate the convergence, accuracy and applicability of the proposed time viscosity-splitting method.

A physics-constrained and data-driven method for modeling supersonic flow

A fast solution of supersonic flow is one of the crucial challenges in engineering applications of supersonic flight. This article introduces a deep learning framework, the supersonic physics-constrained network (SPC), for the rapid solution of unsteady supersonic flow problems. SPC integrates deep convolutional neural networks with physics-constrained methods based on the Euler equation to derive a new loss function that can accurately calculate the flow fields by considering the spatial and temporal characteristics of the flow fields at the previous moment. Compared to purely data-driven methods, SPC significantly reduces the dependency on training data volume by incorporating physical constraints. Additionally, the training process of SPC is more stable than that of data-driven methods. Taking the classic supersonic forward step flow as an example, SPC can accurately calculate strong discontinuities in the flow fields, while reducing the data volume by approximately 60%. In the generalization test experiment for forward step flow and compression ramp flow, SPC also demonstrates good predictive accuracy and generalization capability under different geometric configurations and inflow conditions.

A comparative study of prescribed thermal analysis of a non-Newtonian fluid between exponential and linear porous surfaces

The present study communicates with the thermal analysis of an incompressible micropolar fluid by considering two different prescribed conditions corresponding to two different surfaces. On the porous surface of two different stretchable sheets, the unsteady flow problem of a micropolar fluid is explored by taking the variable impacts of the magnetic field. For both considered sheets, the prescribed thermal analysis is carried out with the contribution of joule heating, viscous dissipation, and radiation. Two prescribed cases of surface temperature and heat flux are discussed for linear stretched surface. Similarly, prescribed cases of exponential surface temperature and exponential heat flux are investigated for the case of an exponential stretchable surface. An effective technique of bvp4c in MATLAB is utilized to numerically tackle the governing equations of the problem. Both the distributions of temperature and velocity and the field of microrotation are graphically scrutinized relative to different geometries and several pertinent parameters. This study of thermal analysis with prescribed conditions elucidates that for an exponential surface, three distributions of flow phenomenon (temperature, microrotation, velocity) manifest more prominent results in comparison to the stretchable surface with linear velocity.

Flow and thermal characteristics of Jeffrey nanofluid in the fixed and moving frames of reference with newly developed Reynolds model

Nanofluids with their excellent thermophysical properties strengthen the thermal performance of an ordinary fluid. Due to the efficacious thermophysical characteristics of nanofluids, the aim of the present study is to discuss the three distinct viscosity models for an incompressible Jeffrey nanofluid relative to its oscillatory oblique stagnation point flow. Three different viscosity models namely Brinkman model, Einstein model, and Reynolds model are discussed to scrutinize the thermophysical attributes of (TiO2-Kerosene oil) nanofluid. The unsteady magnetized flow problem of Jeffrey nanofluid is deliberated over an oscillatory medium corresponding to different frames of references namely fixed frame and moving frame. The thermal analysis is evaluated with the involvement of heat absorption/generation and radiation effects. In both frames of reference, the non-dimensional equations are numerically handled via an efficient technique of bvp4c. The fluid velocity and temperature distribution are graphically compared regarding three distinct viscosity models with numerous pertinent parameters. In the context of all viscosity models, both the distributions of velocity and temperature exhibit excellent behavior in the fixed and moving frame of reference. This study exhibits that the parameter that portrays the ratio of relaxation to retardation times deteriorates the flow field in the fixed frame for all viscosity models.

Validation of wall boundary conditions for simulating complex fluid flows via the Boltzmann equation: Momentum transport and skin friction

The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited the extent of numerical validation studies to simple, often two-dimensional, flow problems. Recent algorithmic advancements for the Boltzmann–Bhatnagar–Gross–Krook equation introduced by the authors [Dzanic et al., J. Comput. Phys. 486, 112146 (2023)], consisting of a highly efficient high-order spatial discretization augmented with a discretely conservative velocity model, have made it feasible to accurately simulate unsteady three-dimensional flow problems across both the rarefied and continuum regimes. This work presents a comprehensive evaluation and validation of wall boundary conditions across a variety of flow regimes, primarily for the purpose of exploring their effects on momentum transfer in the low Mach limit. Results are presented for a range of steady and unsteady wall-bounded flow problems across both the rarefied and continuum regimes, from canonical two-dimensional laminar flows to unsteady three-dimensional transitional and turbulent flows, the latter of which are the first instances of wall-bounded turbulent flows computed by directly solving the Boltzmann equation. We show that approximations of the molecular gas dynamics equations can accurately predict both non-equilibrium phenomena and complex hydrodynamic flow instabilities and show how spatial and velocity domain resolution affect the accuracy. The results indicate that an accurate approximation of particle transport (i.e., high spatial resolution) is significantly more important than particle collision (i.e., high velocity domain resolution) for predicting flow instabilities and momentum transfer consistent with that predicted by the hydrodynamic equations and that these effects can be computed accurately even with very few degrees of freedom in the velocity domain. These findings suggest that highly accurate spatial schemes (e.g., high-order schemes) are a promising approach for solving molecular gas dynamics for complex flows and that the direct solution of the Boltzmann equation can be performed at a reasonable cost when compared to hydrodynamic simulations at the same level of resolution.

Physics-informed neural networks for incompressible flows with moving boundaries

Physics-informed neural networks (PINNs) employed in fluid mechanics deal primarily with stationary boundaries. This hinders the capability to address a wide range of flow problems involving moving bodies. To this end, we propose a novel extension, which enables PINNs to solve incompressible flows with time-dependent moving boundaries. More specifically, we impose Dirichlet constraints of velocity at the moving interfaces and define new loss functions for the corresponding training points. Moreover, we refine training points for flows around the moving boundaries for accuracy. This effectively enforces the no-slip condition of the moving boundaries. With an initial condition, the extended PINNs solve unsteady flow problems with time-dependent moving boundaries and still have the flexibility to leverage partial data to reconstruct the entire flow field. Therefore, the extended version inherits the amalgamation of both physics and data from the original PINNs. With a series of typical flow problems, we demonstrate the effectiveness and accuracy of the extended PINNs. The proposed concept allows for solving inverse problems as well, which calls for further investigations.

Dual solutions for the two-dimension copper oxide with silver (CuO–Αg) and zinc oxide with silver (ΖnO–Αg) hybrid nanofluid flow past a permeable shrinking sheet in a dusty fluid with velocity slip

PurposeThis paper aims to present dual solutions for the two-dimension copper oxide with silver (CuO–Ag) and zinc oxide with silver (ZnO–Ag) hybrid nanofluid flow past a permeable shrinking sheet in a dusty fluid with velocity slip.Design/methodology/approachThe governing partial differential equations for the two dust particle phases are reduced to the pertinent ordinary differential equations using a similarity transformation. Closed-form analytical solutions for the reduced skin friction and reduced Nusselt number, as well as for the velocity and temperature profiles, were presented, both graphically and in tables, under specific non-dimensional physical parameters such as the suction parameter, Prandtl number, slip parameter and shrinking parameter, which are also presented in both figures and tables.FindingsThe results indicate that for the shrinking flow, the wall skin friction is higher in the dusty fluid when compared with the clear (viscous) fluid. In addition, the effect of the fluid–particle interaction parameter to the fluid phase can be seen more clearly in the shrinking flow. Furthermore, multiple (dual, upper and lower branch solutions) are found for the governing similarity equations and the upper branch solution expanded with higher values of the suction parameter. It can be confirmed that the lower branch solution is unstable.Practical implicationsIn practice, the study of the stretching/shrinking flow is crucially important and useful. Both the problems of steady and unsteady flow of a dusty fluid have a wide range of possible applications in practice, such as in the centrifugal separation of particles, sedimentation and underground disposal of radioactive waste materials.Originality/valueEven though the problem of dusty fluid has been broadly investigated, very limited results can be found for a shrinking sheet. Indeed, this paper has succeeded to obtain analytically dual solutions. The stability analysis can be performed by following many published papers on stretching/shrinking sheets. Finally, the critical values and plotting curves for obtaining single or dual solution are successfully presented.

Neural-network-augmented projection-based model order reduction for mitigating the Kolmogorov barrier to reducibility

Inspired by our previous work on a quadratic approximation manifold [1], we propose in this paper a computationally tractable approach for combining a projection-based reduced-order model (PROM) and an artificial neural network (ANN) to mitigate the Kolmogorov barrier to reducibility of parametric and/or highly nonlinear, high-dimensional, physics-based models. The main objective of our PROM-ANN concept is to reduce the dimensionality of the online approximation of the solution beyond what is achievable using affine and quadratic approximation manifolds, while maintaining accuracy. In contrast to previous approaches that exploited one form or another of an ANN, the training of the ANN part of our PROM-ANN does not involve data whose dimension scales with that of the high-dimensional model; and the resulting PROM-ANN can be efficiently hyperreduced using any well-established hyperreduction method. Hence, unlike many other ANN-based model order reduction approaches, the PROM-ANN concept we propose in this paper should be practical for large-scale and industry-relevant computational problems. We demonstrate the computational tractability of its offline stage and the superior wall clock time performance of its online stage for a large-scale, parametric, two-dimensional, model problem that is representative of shock-dominated unsteady flow problems.

CFD Simulation of Low Speed Turbulent Flow Problems Using Unsteady Rans and Large Eddy Simulation Approach

The present paper focuses on the recent development of an implicit pressure-based finite volume algorithm for numerical solution of Navier Stokes equation in an inertial frame of reference for prediction of unsteady incompressible flow problems. The algorithm uses boundary-conforming, multiblock structured grid with moving boundaries, collocated variable arrangement with momentum equations resolved along cartesian directions, second order accurate spatial and temporal discretisation schemes for the convective fluxes and a pressurevelocity solution strategy. Effect of turbulence is simulated using one of the two different approaches. In the Unsteady Reynolds Averaged (URANS) approach coupled to appropriate eddy viscosity based turbulence models, the Navier Stokes (NS) equations, averaged over the whole range of turbulent length scales of the flow, are solved numerically. On the other hand, in the Large Eddy Simulation (LES) approach, the model filtered 3D NS equations are directly solved for the flow variables to resolve the large scale turbulent motions whereas the transport processes at the fine subgrid scale level only are simulated using simple algebraic turbulence model. The capabilities and limitations of both the cost-effective URANS approach and the relatively expensive but rich in physics LES approach have been demonstrated for few application problems of engineering interest.

Numerical and sensitivity study on the heat transfer due to bioconvection on unsteady radiative MHD blood flow over a permeable artery with chemical reaction effects

The primary goal of this research is to investigate the dynamics of nanoparticle-mediated blood flow in the presence of bioconvection effects caused by microorganisms. The boundary layer problem of unsteady magnetohydrodynamic blood flow in the porous medium of tissues in stretching motion is studied. The Casson fluid model of blood flow is mathematically represented by a system of partial differential equations (PDE). The resulting set of governing equations is numerically solved, and the physical interpretation is given for the outcomes that are presented as graphs and tables. The temperature and concentration distribution of blood, along with the organism density profile in the corresponding boundary layer, are plotted, and the effects of various physical parameters, including magnetic field, radiation, chemical reaction, and permeability of the porous medium, on the results are investigated. Additionally, physical effects on the heat and mass transfer coefficients of the flow are also discussed. It is observed that the rate of heat transfer and the temperature profile are improved by increasing the values of the thermophoresis and Brownian motion parameters. Furthermore, at the lowest value of the permeability parameter and the highest value of the Brownian motion factor, the maximum heat transfer rate is observed. The findings of the study bear the promise of significant application in targeted drug delivery, magnetic therapy, and therapeutic hyperthermia treatments.

Unsteady two-phase flow with dirichlet and Robin-type boundary conditions by employing new weber transform

The axisymmetric unsteady two-phase flow problem is explored. The flow domain is defined by two co-axial circular cylinders and is axial symmetric. The Dirichlet-type boundary condition is used on the inner cylindrical surface, whereas the Robin-type boundary condition is used on the outer cylindrical surface. The velocities are computed analytically using a new form of the Weber transform that is suited for these boundary conditions. The effect of the slip parameter on velocities is investigated using numerical simulations and graphical representations. The studied problem is new in the literature because there do not exist any analytical studies regarding the problems with boundary conditions of Dirichlet type on the inner cylinder (the no-slip on the wall) and boundary conditions of Robin type on the outer cylinder (the mixture slipping on the wall). A new integral transform of Weber type has been employed to determine analytical solutions for such problems, together with the Laplace transform. The studied problem could generate analytical solutions for more two-phase flow problems in annular domains since the translational motions of the inner cylinder and the outer cylinder are given by arbitrary functions of the time t.

Solution of filtration problems of construction geotechnology in thin water layers

Filtration problems of construction geotechnics during water movement in thin permeable layers of soils and artificial materials are considered. Under such conditions, traditional approaches borrowed from classical hydrogeology give errors. This is due to the fact that under normal conditions of underground aquifers of a sufficiently large depth, in hydrogeological practice, the hydraulic theory of filtration is used, in which the velocities of filtration currents are averaged along the vertical coordinate. The original nonlinear differential equations of filtration flows are subjected to forced linearization by one or another known method. In this case, the method of linearization by introducing the average power (depth) of the filtration flow is widely used. This method was originally developed for aquifers of great depth. In the presented work, an attempt was made to abandon such a linearization and solve some of the problems of unsteady filtration flows in thin aquifers, which are characteristic of building geotechnics, with obtaining analytical solutions of the final form without introducing artificial simplifications. A methodology is proposed for combining analytical and numerical methods in the process of finding solutions to filtration problems of construction geotechnics with obtaining self-similar dependencies. This approach will make it possible to avoid linearization errors and carry out filtration calculations in thin permeable layers of soils and artificial materials more accurately. A review of domestic and foreign scientific publications on the topic of research has shown some stagnation in this direction. The comparison revealed that in thin permeable layers of soils and artificial materials, preference can be given to filtration calculations using the presented method, since it more accurately describes the non-stationary movement of water in construction geotechnics.

Second-Order Time-Accurate ALE Schemes for Flow Computations with Moving and Topologically Changing Grids

In computations of unsteady flow problems by the arbitrary Lagrangian–Eulerian (ALE) method, the introduction of the grid velocity in the transport terms of the governing equations is not a sufficient condition for conservativeness if topology changes in the dynamic mesh are present and the number of mesh cells changes. We discuss an extension to second-order time differencing schemes (Implicit Euler and Crank–Nicolson) in the finite volume framework, to achieve second-order time-accuracy of the solution. Numerical experiments are given to illustrate the effectiveness of the presented method.

Natural convective heat transfer and fluid flow in a porous medium filled corrugated enclosure: Effect of discrete heat sources

AbstractIn this work, we investigate the two‐dimensional unsteady natural convective fluid flow problem in a porous‐corrugated enclosure with a fixed sinusoidal heated upper wall. The corrugations of the enclosure are discretely heated while vertical walls are maintained isothermally cold. Subject to where the heat sources are located, five different cases are taken into consideration. The vorticity–streamfunction equations are discretized using a transformation‐free higher order compact approach, and the hybrid BiCGSTAB technique is used to solve the system of algebraic equations that derives from the numerical discretization. To validate our findings, we first compare them to previously published numerical and experimental data. The numerically simulated outcomes are then examined over a variety of essential parameters, such as the Darcy (10−5 ≤ Da ≤ 10−1), Rayleigh (103 ≤ Ra ≤ 106), and Prandtl (0.1 ≤ Pr ≤ 10) numbers. Symmetric and asymmetric fluid flow phenomena are observed. Asymmetric flow phenomenon can be caused by miscible or non‐miscible movements of lighter fluids by heavier fluids, or almost exclusively by nonuniform buoyancy‐driven forces caused by density variations that have arisen because of variations in fluid temperature. The averaged Nusselt value for Case 1 and Case 5 exhibits the highest percentage ratio. The thermal boundary layer is strongly affected by compression, dispersion, suppression, the zone of stratification, and the outweighing of isotherms. The simulated results are visualized by stream functions, isotherms, local and averaged Nusselt number plots.

The cooling effect of blood flow during hyperthermia treatment

The amount and duration of the applied heat in hyperthermia treatment are critical for cancer survivors. The challenge is to use a mechanism dealing with the tumor cells only while keeping healthy tissues unharmed. The aim of this paper is to predict the blood temperature distribution in main dimensions during hyperthermia process by deriving a new analytical solution of unsteady flow that adequately covers the cooling factor. We adopted a separation of variable method to solve the bio-heat transfer problem of unsteady blood flow. The solution is similar to Pennes’ equation, except that it is for blood rather than tissue. We also performed computational simulations with varied flow conditions and thermal energy transports. The blood cooling effects were calculated with vessel’s diameter, tumor’s zone length, pulsating period and flow velocity. The cooling rate rises by around 133% if the tumor zone’s length is extended four times the diameter of 0.5 (mm), but it is seemingly fixed with this distance if the diameter is equal or larger than 4 (mm). Likewise, the temporal variations of temperature disappear if the blood vessel has a diameter of 4 (mm) or more. Pre-heating or post-cooling techniques perform effectively given the theoretical solution; under particular conditions, the reduction percentages of the cooling effect are between 130% and 200%, respectively.