Case Of Unsteady Flow Research Articles

Experimental Establishing of Moving Hydraulic Jump in a Trapezoidal Channel

This research was prepared as a preliminary laboratory study to achieve a moving hydraulic jump with controlled discharges. It is an initial part of the study that is being prepared to treat the salt tide occurring in the Shatt al-Arab due to the lack of water imports that were coming from the Karun and Karkheh rivers from Iranian territory, as this scarcity caused a salt tide that affected significantly the environmental reality of the city of Basra and the agricultural lands surrounding the Shatt al-Arab, such as the Shatt al-Arab district and the Siba orchards. As part of the proposed solutions, a moving hydraulic jump is created that pushes the salt tongue into the Persian Gulf; the results were promising. A moving hydraulic leap is a good example of unstable super- and sub-critical flow regimes and is regarded as a specific case of unsteady flow in a channel. There aren't many published experiments on this particular flow type, and the quantitative simulation of such a flow state has some inherent complexity. An experimental setup was created for this work in order to assess the hydraulic performance of a moving hydraulic jump in a trapezoidal flume. A sluice gate was installed at the flume's upstream edge to provide an unstable supercritical flow regime, movable hydraulic jumps along the channel, and temporal water stages at the gate's upstream side for the various downstream end boundary situations. Several flow factors, including energy head, pressure head, and flow depth, were estimated from the recorded data. The study found connections between discharge and shifting hydraulic jump variables. By employing relatively stable momentum and energy formulas, simple and time-independent formulas were developed that accurately predicted the pressure head in the subcritical region of an unstable mixed flow. As a result, the moving hydraulic jump factor can be correctly predicted using time-independent correlations by using the discharge variation as a boundary scenario. Doi: 10.28991/CEJ-2023-09-04-08 Full Text: PDF

Towards a novel EMHD dissipative stagnation point flow model for radiating copper-based ethylene glycol nanofluids: An unsteady two-dimensional homogeneous second-grade flow case study

A novel EMHD dissipative second-grade nanofluid flow model is proposed exclusively in this numerical inspection for radiating copper-based ethylene glycol nanofluids to reveal the dynamical and thermal aspects of the studied homogeneous mixture during its unsteady two-dimensional stagnation point flow towards a horizontal electromagnetic actuator. Based on admissible physical assumptions and authenticated experimental correlations, the governing PDEs and BCs are derived appropriately for the nanofluid flow problem under consideration. After numerous rearrangements and non-dimensionalization treatments, the resulting ODEs and BCs are handled computationally with the help of a robust GDQ algorithm under the parametric control of several influencing factors, whose strengthening magnitudes affect probably the flow control process and heat transport mechanism. In this context, it proved graphically that the nanoparticles’ loading process exhibits dissimilar dynamical and thermal impacts as compared with the influences of the nanoparticles’ diameter size. Besides, the resistive dynamical effect of the utilized electromagnetic actuator reinforces thermally the enhancing role of the thermal radiative heat flux and Joule’s heating process within the nanofluidic medium.

Experimental and Theoretical Study of Surge Behavior in a Boil-Off Gas Centrifugal Compressor on an LNG Carrier

In this study, we conducted experiments and numerical analysis on a 270 kW industrial-scale centrifugal compressor used in the fuel supply system of an LNG carrier in order to improve the lumped-parameter surge model by considering the viscosity in the pipeline and to confirm whether the improved model would be applicable. The steady and unsteady compressor performance curves were constructed using measurements and predictions, respectively. The flow through the pipeline was assumed to be both steady and unsteady, and each governing equation under the assumptions was derived in accordance with the lumped-parameter model. In the steady flow case, the surge behavior of the modified model was in a good agreement with the lumped-parameter model at surge parameter B = 4.8716. In the unsteady flow case, however, the modified model showed a deviation from the lumped-parameter model, and the simulation from the modified model described the surge behavior 5% more accurately than the lumped-parameter model. Through experiments and numerical analysis, this study showed that the present models are useful and applicable for describing the surge behavior of an industrial-scale single-stage centrifugal compressor.

A machine learning approach for propeller design and optimization: Part II

We propose and analyse an optimization method that uses a machine learning approach to solve multi-objective, constrained propeller optimization problems. The method uses an online learning strategy where explainable supervised classifiers learn the location of the Pareto front and advise search strategies. The classifiers are trained with orthogonal features that capture geometric variation in radial distribution of pitch, skew, camber and chordlength. Based on orthogonal features, the classifiers predict whether or not a design lies on the Pareto front. If the design is predicted to lie on the Pareto front, the method verifies this with an evaluation. If the design is predicted to not lie on the Pareto front with a high confidence level, then the design is ignored. This skipped evaluation reduces the computational effort of optimization. The method is demonstrated on a cavitating, unsteady flow case of the Wageningen B-4 70 propeller with P/D = 1.0 operating in the Seiun-Maru wake. Compared to the classical Non-dominated Sorting Genetic Algorithm — III (NSGA-III) the optimization method is able to reduce 30% of evaluations per generation while reproducing a comparable Pareto front. Trade-offs between suction side, pressure side, tip-vortex cavitation and efficiency are identified from the Pareto front. The non-elitist NSGA-III search algorithm in conjunction with the explainable supervised classifiers also find very diverse solutions. Among the solutions, a design with no pressure side cavitation, low suction side cavitation and reasonable tip-vortex cavitation is found.

Unsteady MHD free convective flow past a vertical plate: An automated solution approach

The case of unsteady two-dimensional laminar free convection flow over a vertical plate by an incompressible viscous fluid is analysed in the presence of uniform magnetic field perpendicular to the flow. The governing equations in a vector form are transformed into non- dimensional form. Then, the dimensionless equations are solved using automated solution technique which is FEniCS. The effects of magnetic parameter on the velocity and temperature profiles are obtained and discussed in this paper

Experimental investigation of gradually-varied unsteady flow passed a circular pile

The flow field around a vertically mounted circular pile exposed to gradually-varied unsteady flow is experimentally investigated. Experiments were conducted in a 30 m-long and 1 m-wide recirculating flume equipped with a variable discharge pump. A circular cylinder with 9 cm diameter was used as the model pile. To understand the influence of accelerating and decelerating flow conditions, three unsteady cases with different unsteadiness degrees were tested as well as a reference steady flow case. The spatial and temporal variations of Reynolds-averaged velocity and turbulence characteristics around the pile, as well as undisturbed flow, were analyzed. Findings show that there are distinct differences between the tested gradually-varied unsteady flow cases and the reference steady flow case. The Reynolds-averaged velocity vs. TKE plots of undisturbed flow indicated a hysteresis effect, such that larger turbulence is generated during the falling stage of the flow compared to the rising stage. This hysteresis was considerably reduced in the pile wake, and even reversed hysteresis was seen at certain cases. The spatial variation of Reynolds-averaged velocity and turbulence in the peak instant of unsteady flow was qualitatively similar to that of steady flow, but quantitatively, turbulence, flow contraction, and velocity deficit in the near-wake region were smaller in the case of unsteady flow. Contrarily, the unsteady flow generated remarkably higher turbulence levels at further downstream in the pile wake. It is concluded that in the case of unsteady flow the pile behaves as if it has a more streamlined shape. The results were also interpreted from structure-bed interactions perspective, explaining the differences between the pile scour induced by steady and unsteady flow conditions.

Unsteady MHD Mixed Convection Flow of Water over a Sphere with Mass Transfer

This paper examines the unsteady magnetohydrodynamic (MHD) mixed convection flow over a sphere combined with variable fluid properties. An implicit finite difference scheme, together with the quasi-linearization, is used to find non-similar solutions for the governing equations. The vanishing skin friction is prevented or at least delayed by enhancing the mixed convection in both the cases of steady and unsteady fluid flow. Both skin friction and heat transfer coefficients are found to be increasing with an increase in time or MHD parameter.

Objective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows.

Computing and visualizing features in fluid flow often depends on the observer, or reference frame, relative to which the input velocity field is given. A desired property of feature detectors is therefore that they are objective, meaning independent of the input reference frame. However, the standard definition of objectivity is only given for Euclidean domains and cannot be applied in curved spaces. We build on methods from mathematical physics and Riemannian geometry to generalize objectivity to curved spaces, using the powerful notion of symmetry groups as the basis for definition. From this, we develop a general mathematical framework for the objective computation of observer fields for curved spaces, relative to which other computed measures become objective. An important property of our framework is that it works intrinsically in 2D, instead of in the 3D ambient space. This enables a direct generalization of the 2D computation via optimization of observer fields in flat space to curved domains, without having to perform optimization in 3D. We specifically develop the case of unsteady 2D geophysical flows given on spheres, such as the Earth. Our observer fields in curved spaces then enable objective feature computation as well as the visualization of the time evolution of scalar and vector fields, such that the automatically computed reference frames follow moving structures like vortices in a way that makes them appear to be steady.

Aerodinamika talasaste lopatice pod uticajem fluktuirajućeg protoka vetra

In the present study, the influence of the wavy edge blade on aerodynamic characteristics for the flow of blades at Reynolds number (Re) of 8×105 is numerically investigated based on the unsteady wind flow. Aerodynamic characteristics of a (sinusoidal leading edge) wavy NACA0015 aerofoil blade are carried out using ICEM 19.1 and ANSYS fluent. The numerical simulation is conducted then validated by experimental data with steady wind flow. This is conducted by employing the same Reynold's number in the experimental work. While, the unsteady flow was numerically performed at 1 Hz frequency of wind flow conditions. The main findings from this work show that the wavy blade can behave better in turbulent wind conditions with the maximum lift coefficient of 0.73 compared to 0.621 for the normal blade. However, the findings declare that the wavy blade stalled earlier than the normal one in the unsteady flow case. Similarly, it stalled at 12° angle of attack earlier than the normal one which was stalled at 14° in the steady flow case.

Dynamic mode decomposition with exogenous input for data-driven modeling of unsteady flows

This work proposes a data-driven reduced-order modeling algorithm for complex, high-dimensional, and unsteady fluid systems with exogenous input and control. This algorithm is a variant of dynamic mode decomposition (DMD), which is an equation-free method for identifying coherent structures and modeling complex flow dynamics. Compared with existing methods, the proposed method improves the capability of predicting the flow evolution near the unstable equilibrium state. The method is achieved by two steps. First, the system matrix without input is identified by standard DMD to represent the intrinsic flow dynamics. Second, the input term, represented by a state space equation, is identified through existing methods for DMD with control effects. The whole system with input is described by the superposition of both the system matrix and the input term. The proposed method is validated by one simple two-dimensional dynamic system and two test cases of unsteady flow, including flow past a circular cylinder at Reynolds number 45 and flow past a NACA0012 airfoil at an angle of attack 25°. Results indicate that the proposed method gives more accurate description on the flow evolution with or without external forcing.

Second Law Analysis of Unsteady MHD Viscous Flow over a Horizontal Stretching Sheet Heated Non-Uniformly in the Presence of Ohmic Heating: Utilization of Gear-Generalized Differential Quadrature Method.

In this article, the entropy generation characteristics of a laminar unsteady MHD boundary layer flow are analysed numerically for an incompressible, electrically conducting and dissipative fluid. The Ohmic heating and energy dissipation effects are added to the energy equation. The modelled dimensional transport equations are altered into dimensionless self-similar partial differential equations (PDEs) through suitable transformations. The reduced momentum and energy equations are then worked out numerically by employing a new hybrid method called the Gear-Generalized Differential Quadrature Method (GGDQM). The obtained numerical results are incorporated in the calculation of the Bejan number and dimensionless entropy generation. Quantities of physical interest, like velocity, temperature, shear stress and heat transfer rate, are illustrated graphically as well as in tabular form. Impacts of involved parameters are examined and discussed thoroughly in this investigation. Exact and GGDQM solutions are compared for special cases of initial unsteady flow and final steady state flow. Furthermore, a good harmony is observed between the results of GGDQM and those given previously by the Spectral Relaxation Method (SRM), Spectral Quasilinearization Method (SQLM) and Spectral Perturbation Method (SPM).

Numerical simulation of unsteady flows through a radial turbine

The article deals with the numerical simulation of unsteady flows through the turbine part of the turbocharger. The main focus of the article is the extension of the in-house CFD finite volume solver for the case of unsteady flows in radial turbines and the coupling to an external zero-dimensional model of the inlet and outlet parts. In the second part, brief description of a simplified one-dimensional model of the turbine is given. The final part presents a comparison of the results of numerical simulations using both the 3D CFD method and the 1D simplified model with the experimental data. The comparison shows that the properly calibrated 1D model gives accurate predictions of mass flow rate and turbine performance at much less computational time than the full 3D CFD method. On the other hand, the more expensive 3D CFD method does not need any specific calibration and allows detailed inspections of the flow fields.

Solution-based adaptive mesh redistribution applied to harmonic balance solvers

A primary source of inaccuracy in numerical simulations is due to errors that are introduced into the solution via the discretization of the continuous governing equations over the computational domain. By increasing the grid resolution in regions with high flow gradients and large curvatures using a solution-adaptive approach, these discretization errors can be reduced. In this paper, an adaptive mesh technique is presented that can efficiently cluster the grid nodes in sensitive regions by redistribution and relocation of the grid nodes. This adaptive technique is specifically important to unsteady periodic flow cases where the length scales of the flow features (such as shocks, boundary layer, and separation zones) can differ between time instances. The proposed technique is developed – for the first time in the literature – for a harmonic balance method to efficiently model unsteady periodic flows. To study the performance of the proposed technique in improving the accuracy of the flow solver, steady and unsteady flow cases are studied. Numerical results show that the adaptive mesh redistribution technique is capable of efficiently increasing the accuracy of the numerical solver with a relatively low computational overhead.

Depth-averaged velocity and bed shear stress in unsteady open channel flow over rough bed

Very few studies have been carried out in the past in estimating depth-averaged velocity and bed shear stress in unsteady flow over rough beds. An experiment is thus conducted to investigate the vertical and lateral velocity profiles under unsteady flow conditions in a rough open channel for various flow depths. One hydrogram is repeatedly passed through the rectangular flume with a fixed rigid grass bed. Using micro Pitot tube and Acoustic Doppler Velocimeter (ADV), the flow patterns are investigated at both lateral and longitudinal positions over different cross-sections. For two typical flow depths, the velocities in both the rising limb and falling limb are observed. Hysteresis effect between stage-discharge (h ~ Q) rating curve between rising and falling limbs is illustrated. Lateral distribution of depth-averaged velocity and bed shear stress are plotted at three different cross sections and compared with the steady flow conditions. In falling limb of an unsteady flow case, both depth-averaged velocity and bed shear stress distribution in the central region is higher than that of steady flow case. However, in the rising limb, the bed shear stress of unsteady flow is less than that of steady flow case. Further, in an unsteady flow, the magnitude of depth-averaged velocity is found to increase towards the downstream sections. Along the downstream positions, bed shear stress values increase for lower flow depths and decrease for higher flow depth cases.

Prediction of discretization error using the error transport equation

This study focuses on an approach to quantify the discretization error associated with numerical solutions of partial differential equations by solving an error transport equation (ETE). The goal is to develop a method that can be used to adequately predict the discretization error using the numerical solution on only one grid/mesh. The primary problem associated with solving the ETE is the formulation of the error source term which is required for accurately predicting the transport of the error. In this study, a novel approach is considered which involves fitting the numerical solution with a series of locally smooth curves and then blending them together with a weighted spline approach. The result is a continuously differentiable analytic expression that can be used to determine the error source term. Once the source term has been developed, the ETE can easily be solved using the same solver that is used to obtain the original numerical solution. The new methodology is applied to the two-dimensional Navier–Stokes equations in the laminar flow regime. A simple unsteady flow case is also considered. The discretization error predictions based on the methodology presented in this study are in good agreement with the ‘true error’. While in most cases the error predictions are not quite as accurate as those from Richardson extrapolation, the results are reasonable and only require one numerical grid. The current results indicate that there is much promise going forward with the newly developed error source term evaluation technique and the ETE.

Aeroacoustic’s Investigation on High-Lift Device by using a Modern Hybrid RANS/LES-Model

This study focuses on the development, validation and application of the interdisciplinary computational fluid dynamics/computational aeroacoustics (CFD/CAA) method with the name Flight-Physics Simulator AEOLus (FPSAEOLus). FPS-AEOLus is based on enhanced conservative, anisotropic, hybrid Reynolds-averaged Navier-Stokes/ Large-Eddy Simulation (RANS/LES) techniques to solve an aerodynamic flow field by applying the unsteady, compressible, hyperbolic Navier–Stokes equations of second order. The two-layer SSG/LRR- ω differential Reynolds stress turbulence model presented, combining the Launder- Reece-Rodi (LRR) model near walls with the Speziale-Sarkar-Gatski (SSG) model further apart by applying Menter's blending function F1. Herein, Menter's baseline ω-equation is exploited for supplying the length scale. Another emphasis is put on the anisotropic description of dissipation at close distance to the solid wall or in wake area for describing the friction-induced surface-roughness behaviour in viscous fluid physics and swirling wake effects. For that purpose, the SSG/LRR-ω seven-equations Reynolds stress turbulence model with anisotropic extension was realized, therefor the theory is described in general. Beyond that, a modified delayed detached-eddy simulation (MDDES) and a scale adaptive simulation (SAS) correction to capture the stochastic character of a large-eddy-type unsteady flow with massive flow separations in the broad band is implemented. To demonstrate the time-dependent noise propagation having wave interference a linearized Euler equation (LEE) model using a combined Momentum- and Lamb-vector source have been applied into the CFD/CAA - method. The DLR 15 wing, a High-Lift device in landing configuration having a deployed slat and landing flap is studied experimentally and numerically. The first part of the application deals with the steady flow investigation; however, the same turbulence model is used for the unsteady flow case without the enclosed time derivatives. The second part concentrates on unsteady modelling for the Navier–Stokes and Linearized Euler field. With this new combined CFD/CAA - method, steady and unsteady numerical studies for the high-lift wing configuration for discovering the aerodynamic and –acoustic propagation effects are shown, discussed and when experimental data were available validated. The High-Lift wing has a constant sweep angle of Λ=30° to investigate possible cross-flow; to realize this, periodic boundary conditions were set in spanwise direction

The Formation of Counter-Rotating Vortex Pair and the Nature of Liftoff-Reattachment in Film-Cooling Flow

Traditionally, the formation of the Counter-Rotating Vortex Pair (CRVP) has been attributed to three main sources: the jet-mainstream shear layer where the jet meets with the mainstream flow right outside the pipe, the in-tube boundary layer developing along the pipe wall, and the in-tube vortices associated with the tube inlet vorticity; whereas the liftoff-reattachment phenomenon occurring in the main flow along the plate right downstream of the jet has been associated with the jet flow trajectory. The jet-mainstream shear layer has also been demonstrated to be the dominant source of CRVP formation, whereby the shear layer disintegrates into vortex rings that deform as the jet convects downstream, becoming a pair of CRVPs flowing within the jet and eventually turning into the main flow direction. These traditional findings are assessed qualitatively and quantitatively for film-cooling flow in gas turbines by simulating numerically the flow and evaluating the extent to which the traditional flow phenomena are taking place particularly for CRVP and for flow liftoff-reattachment. To this end, three flow simulation cases are used; they are referred to as 1—the baseline case; 2—the free-slip in-tube wall case (FSIT); and 3—the unsteady flow case. The baseline case is a typical film-cooling case. The FSIT case is used to assess the in-tube boundary layer. Cases 1 and 2 are simulated using the Reynolds-averaged Navier-Stokes equations (RANS), whereas Case 3 solves a Detached Eddy Simulation (DES) model. It is concluded that decreasing the strength of the CRVP, which is the case for e.g., shaped holes, provides high cooling performance, and the liftoff-reattachment phenomenon was thus found to be strongly influenced by the entrainment caused by the CRVP, rather than the jet flow trajectory. These interpretations of the flow physics that are more relevant to gas turbine cooling flow are new and provide a physics-based guideline for designing new film-cooling schemes.

Results of the AVATAR project for the validation of 2D aerodynamic models with experimental data of the DU95W180 airfoil with unsteady flap

The FP7 AdVanced Aerodynamic Tools for lArge Rotors - Avatar project aims to develop and validate advanced aerodynamic models, to be used in integral design codes for the next generation of large scale wind turbines (10-20MW). One of the approaches towards reaching rotors for 10-20MW size is the application of flow control devices, such as flaps. In Task 3.2: Development of aerodynamic codes for modelling of flow devices on aerofoils and, rotors of the Avatar project, aerodynamic codes are benchmarked and validated against the experimental data of a DU95W180 airfoil in steady and unsteady flow, for different angle of attack and flap settings, including unsteady oscillatory trailing-edge-flap motion, carried out within the framework of WP3: Models for Flow Devices and Flow Control, Task 3.1: CFD and Experimental Database. The aerodynamics codes are: AdaptFoil2D, Foil2W, FLOWer, MaPFlow, OpenFOAM, Q3UIC, ATEFlap. The codes include unsteady Eulerian CFD simulations with grid deformation, panel models and indicial engineering models. The validation cases correspond to 18 steady flow cases, and 42 unsteady flow cases, for varying angle of attack, flap deflection and reduced frequency, with free and forced transition. The validation of the models show varying degrees of agreement, varying between models and flow cases.

A new hybrid mechanism for dynamic wind tunnel test of high maneuverable air vehicle

A new dynamic test mechanism has been developed in the unsteady low-speed wind tunnel at Nanjing University of Aeronautics and Astronautics to enhance the abilities of experiments in the unsteady flow cases. The structure of the new test mechanism is described in detail in this paper and the equations used to control the performance of test model’s motions are also listed here. Then a wing-body model was tested in the new test system for the first time, including the forced oscillation tests and free-to-roll test at high angle of attack region. The test results are also discussed.

High-order implicit time integration for unsteady turbulent flow simulations

Higher order explicit diagonal Runge–Kutta (EDIRK) schemes are investigated for their applicability to realistic unsteady turbulent flow simulations. A second order, two new third order accurate schemes with different stage order accuracy, and a fourth order accurate scheme are tested and compared to the commonly used implicit second order backward difference (BDF2) method. All methods are implemented in a flow solver for unstructured grids where the non-linear equations from the implicit temporal discretizations are formulated as a steady state problem which is solved by standard techniques for steady flow problems. The main objective for the comparison is the accuracy and efficiency of the methods but the influence of different steady state convergence criteria is also addressed. The time integrators are evaluated on van der Pol’s equations and unsteady laminar and turbulent flow cases in two and three dimensions. The design orders for all schemes are verified for all test cases except the fourth order scheme for a turbulent case which is approximately third order with increasing accuracy as the time step is refined. The second order schemes are more efficient for larger time steps. Due to lower truncation error, the second order EDIRK scheme is equally or more efficient than the BDF2 scheme although one additional implicit stage is involved per time step. The higher order (⩾3) schemes become more competitive with smaller time steps and are often more efficient than the second order schemes.