Analysis Of Unsteady Flow Research Articles

Comparison of solutions of Saint-Venant equations by characteristics and finite difference methods for unsteady flow analysis in open channel

Comparison of solutions of Saint-Venant equations by characteristics and finite difference methods for unsteady flow analysis in open channel

Comparison of solutions of Saint-Venant equations by characteristics and finite difference methods for unsteady flow analysis in open channel

The unsteady flow can be analysed by Saint-Venant equations. These equations can be solved by characteristics and finite difference methods. The Saint-Venant equations are changed into four complete differential equations in characteristics method and these equations are solved by drawing two characteristics lines. The Saint-Venant equations are changed into set nonlinear equations and are solved using Preissman scheme in finite difference method. This set of equation is changed into linear equation using Newton-Rafson method and can be solved using Sparce method. In this research, the results of the two method were compared and this was shown that: 1) these two methods can draw the surface profiles and flow hydrograph as well; 2) the finite difference method is more accurate than that one; 3) the mesh size in finite difference method can be larger than that one; 4) the difference between two methods are increased by increasing the time and distance.

Numerical and Experimental Research on Aerodynamic Noise Characteristics of a Multi-Blade Centrifugal Fan

The aerodynamic noise characteristic of a multi-blade centrifugal fan was studied by using numerical analysis and experimental test methods respectively. The unsteady flow dynamics analysis method and aeroacoustics based on finite element method were used to predict the spectral characteristics of noise of the fan. And then the spectral characteristic of noise of the centrifugal fan was measured in a semianechoic room. A good match was obtained respectively by using the numerical analysis and the experimental test. Based on this work, for now, the numerical analysis method of aerodynamic noise can be used to judge qualitatively the noise level of multi-blade centrifugal fans by adjusting the unsteady flow analysis model.

Unsteady Flow and Pressure Pulsation Characteristics Analysis of Rotating Stall in Centrifugal Pumps Under Off-Design Conditions

Unsteady flow phenomena like rotating stall frequently occur in centrifugal pumps under off-design conditions. Rotating stall could lead to flow instabilities and pressure pulsation, which affect the normal operation of pumps. The mechanism of rotating stall has not been sufficiently understood in previous researches. In this study, the impact of rotating stall in the impeller on centrifugal pump stability and pressure pulsation is numerically investigated. This paper aims to detect the unsteady flow characteristics inside the centrifugal pump by computational fluid dynamics technology, to analyze pressure pulsations caused by rotating stall and to explore the propagation mechanism of rotating stall. Unsteady numerical simulations are performed by ANSYS 16.0 to model the unsteady flow within the entire flow passage of a centrifugal pump under 0.4QBEP and 0.6QBEP working conditions. Through flow characteristics research, the generation and propagation of rotating stall are discovered. Flow separation appears near the leading edge of the pressure side and transforms into vortices, which move along the passage. Meanwhile, the stall cells rotate circumferentially in the impeller. Additionally, frequencies and amplitudes of pressure pulsations related to rotating stall are investigated by spectrum analysis. The results detect a possible characteristic frequency of rotating stall and show that the interaction between stall cells and the volute tongue could have an influence on rotor–stator interaction (RSI).

NUMERICAL SOLUTION OF UNSTEADY FLOW BETWEEN PARALLEL PLATES USING HAAR WAVELET-QUASILINEARIZATION METHOD

The present study is concerned with the analysis of unsteady flow of viscous incompressible fluid between parallel rectangular and circular plates. The Navier-Stokes equations modelling the flow are transformed into a fourth order non-linear ordinary differential equation using a similarity transformation. The resulting equation is solved by a new efficient numerical scheme based on Haar wavelet-quasilinearization method. The solution representing pressure gradient is obtained for large values of Reynolds number. A comparison with numerical results generated by MATLAB routine bvp4c demonstrates that the proposed method is more efficient and promising technique for solving highly nonlinear two-point boundary value problems. The absolute error and rate of convergence of numerical results are computed to test the applicability and accuracy of the method

Singular perturbation and differential transform methods to two-dimensional flow of nanofluid in a porous channel with expanding/contracting walls subjected to a uniform transverse magnetic field

This paper presents a comparative study of two approximate analytical methods for the analysis of two-dimensional unsteady flow of nanofluid in a porous channel through expanding/contracting walls with large injection or suction under the influence of a uniform transverse magnetic field. Similarity transformations are used to reduce the systems of the governing partial differential equations to a nonlinear fourth-order ordinary differential equation which is solved using method of matched asymptotic expansion and differential transform method. From the verification of the approximate analytical solutions, it is established that the results obtained using differential transformation method demonstrate remarkable accuracy and better agreements with the results of numerical method than the results obtained using method of matched asymptotic expansion. Therefore, the differential transform method gives more accurate results than method of matched asymptotic expansion. Also, due to the higher accuracy of the differential transformation method than the method of matched asymptotic expansion, the approximate analytical solutions through the differential transformation method are used to investigate the effects of permeation Reynolds number, wall expansion ratio and magnetic parameter on the flow behavior of the fluid. From the results, it is established that increase in the Reynolds number decreases the axial velocity at the center of the channel during the expansion while the axial velocity increases slightly near the surface of the channel when the wall contracts at the same rate. Also, as the wall expansion ratio increases, the velocity at the center decreases and increases near the wall. For every level of injection or suction, in the case of expanding wall, increasing the wall dilation rate leads to increase in axial velocity near the center and decrease in the axial velocity near the wall. The results present in this work can serve as references for the other methods of analysis of the problem.

A complete rotor–stator coupling method for frequency domain analysis of turbomachinery unsteady flow

The paper presents a rotor–stator coupling method for analyzing unsteady flow field within multi-blade-row turbomachines using a frequency domain method. The coupling method is called time and space mode decomposition and matching method. It is based upon coordinate transformation and Fourier transformation to extract relevant time and space modes represented by frequency of unsteadiness, nodal diameter and Fourier coefficients. Detailed procedures together with relevant formula are established to identify the matching time and space modes across an interface and calculate corresponding mode coefficients. The mode coefficients are then matched across an interface with the use of a one-dimensional non-reflective implementation. To verify the correctness and effectiveness of the proposed interface treatment, a transonic compressor was used as a test case. The unsteady flow field within it was analyzed using a time domain time marching method to obtain the results as a reference. Then various frequency domain solutions with different resolution of unsteady frequencies were performed. Comparison of amplitude of different static pressure harmonics between frequency domain solutions and the reference time domain solution was made and discussed.

Heat transfer analysis of fractional second-grade fluid subject to Newtonian heating with Caputo and Caputo-Fabrizio fractional derivatives: A comparison

The present study is a comparative analysis of unsteady flows of a second-grade fluid with Newtonian heating and time-fractional derivatives, namely, the Caputo fractional derivative (singular kernel) and the Caputo-Fabrizio fractional derivative (non-singular kernel). A physical model for second-grade fluids is developed with fractional derivatives. The expressions for temperature and velocity fields in dimensionless form as well as rates of heat transfer are determined by means of the Laplace transform technique. Solutions for ordinary cases corresponding to integer order derivatives are also obtained. Numerical computations for a comparison between the solutions of the problem with the Caputo time-fractional derivative, problem with Caputo-Fabrizio time-fractional derivative and of the ordinary fluid problem were made. The influence of some flow parameters and fractional parameter $\alpha$ on temperature field as well as velocity field was presented graphically and in tabular forms.

Conservation of time scale for one-dimensional pulsating flow

In the work by analysis of one-dimensional unsteady flows, based on the fundamental law of conservation with application of Fourier series is shown that in the presence of periodic, steady pulsations along the flow, the main frequency as well as all higher frequencies remain constant and only the amplitude of oscillations is changed that is in full agreement with the results of analysis of more complex three-dimensional flows. Thus, is confirmed the validity of the principle of conservation of frequencies or time scale along the flow. So, is obtained very interesting result for turbulence problem solution.

Extension of the Non-Linear Harmonic method for the study of the dynamic aeroelasticity of horizontal axis wind turbines

In this paper an innovative methodology for the study of horizontal axis wind turbines dynamic aeroelasticity is presented. It can be understood as an extension of the Non-Linear Harmonic (NLH) method, an efficient computational approach for the analysis of unsteady periodic flows. A linearized model of the structure consisting of a set of mode shapes and natural frequencies was included. The aeroelastic equilibrium was ensured through a set of equations linking the structural displacements and the fluid loads for both the time-averaged and the harmonic contributions. First, the developed methodology is tested in the framework of a 2D cylinder mounted on a single degree of freedom elastic system and undergoing Vortex Induced Vibrations (VIV). The results are compared with previous experimental and computational studies, revealing the potential of the method for the prediction of both the shedding frequency and the aeroelastic response. Secondly, the dynamic aeroelasticity of the complete DTU 10MW RWT wind turbine (i.e. including the tower) is assessed. A nominal operating point is studied, and the rotor flexibility is considered via a blade structural model. The results of this Fluid–Structure Interaction (FSI) simulation are compared with two additional computations, both assuming rigid blades, that modeled the isolated DTU 10MW RWT rotor and the complete machine. This allowed to distinguish the impact of the blade flexibility on the rotor performance from the potential effects associated to the presence of the tower. In particular, the consideration of the aeroelasticity led to a decrease of the predicted time-averaged rotor loads and the corresponding amplitudes of oscillation. For its application on the DTU 10MW RWT, the developed methodology was found to be one order of magnitude faster than a standard time marching approach.

Effect of rotation on the flow behaviour in a high-speed cryogenic microturbine used in helium applications

The complex flow characteristics in a high-speed helium microturbine used in cryogenic refrigeration and liquefaction cycles are highly influenced by the effects of rotation. In order to enhance the turbine performance and to improve the preliminary design process of the turboexpander, the flow characteristics within the turbine blade passage need to be investigated at different rotational speeds. Here, three-dimensional unsteady flow analysis of a high speed cryogenic microturbine used in helium applications was carried out using Ansys CFX®. The loss generated by the various secondary and vortical flows for the different cases was quantified in terms of entropy loss coefficient. The loss generating mechanism was also assessed by analysing the velocity vectors, entropy contours and the behaviour of the vortex cores. With change in speed the influence of scraping flow due to relative casing motion and the blade loading on the flow characteristics was found to vary significantly. At lower speeds, the scraping flow decreases and thus augments the tip leakage flow which in turn interacts with the suction side leg of the leading edge vortex to form a single large vortex. This combined vortex increases the velocity defect and thus leads to increased loss generation. The analysis of the vortex core velocity and the blade loading diagram revealed the need for modifications in blade profile for improved turbine performance. Furthermore, the comparison of the CFD results with the Balje's nsds chart showed remarkable variations, the results of which can be used to modify the chart for the design of efficient cryogenic microturbines for helium applications.

Analysis of unsteady flow over Offshore Wind Turbine in combination with different types of foundations

Environmental effects have an important influence on Offshore Wind Turbine (OWT) power generation efficiency and the structural stability of such turbines. In this study, we use an in-house Boundary Element (BEM)—panMARE code—to simulate the unsteady flow behavior of a full OWT with various combinations of aerodynamic and hydrodynamic loads in the time domain. This code is implemented to simulate potential flows for different applications and is based on a three-dimensional first-order panel method. Three different OWT configurations consisting of a generic 5 MW NREL rotor with three different types of foundations (Monopile, Tripod, and Jacket) are investigated. These three configurations are analyzed using the RANSE solver which is carried out using ANSYS CFX for validating the corresponding results. The simulations are performed under the same environmental atmospheric wind shear and rotor angular velocity, and the wave properties are wave height of 4 m and wave period of 7.16 s. In the present work, wave environmental effects were investigated firstly for the two solvers, and good agreement is achieved. Moreover, pressure distribution in each OWT case is presented, including detailed information about local flow fields. The time history of the forces at inflow direction and its moments around the mudline at each OWT part are presented in a dimensionless form with respect to the mean value of the last three loads and the moment amplitudes obtained from the BEM code, where the contribution of rotor force is lower in the tripod case and higher in the jacket case and the calculated hydrodynamic load that effect on jacket foundation type is lower than other two cases.

Solution Stabilization and Convergence Acceleration for the Harmonic Balance Equation System

This paper presents an efficient approach for stabilizing solution and accelerating convergence of a harmonic balance equation system for an efficient analysis of turbomachinery unsteady flows due to flutter and blade row interaction. The proposed approach combines the Runge–Kutta method with the lower upper symmetric Gauss Seidel (LU-SGS) method and the block Jacobi method. The LU-SGS method, different from its original application as an implicit time marching scheme, is used as an implicit residual smoother with under-relaxation, allowing big Courant–Friedrichs–Lewy (CFL) numbers (in the order of hundreds), leading to significant convergence speedup. The block Jacobi method is introduced to implicitly integrate the time spectral source term of a harmonic balance equation system, in order to reduce the complexity of the direct implicit time integration by the LU-SGS method. The implicit treatment of the time spectral source term thus greatly augments the stability region of a harmonic balance equation system in the case of grid-reduced frequency well above ten. Validation of the harmonic balance flow solver was carried out using linear cascade test data. Flutter analysis of a transonic rotor and blade row interaction analyses for a transonic compressor stage were presented to demonstrate the stabilization and acceleration effect by the combination of the LU-SGS and the block Jacobi methods. The influence of the number of Jacobi iterations on solution stabilization is also investigated, showing that two Jacobi iterations are sufficient for stability purpose, which is much more efficient than existing methods of its kind in the open literature.

Perturbation analysis of unsteady boundary layer slip flow and heat transfer of Casson fluid past a vertical permeable plate with Hall current

The current study focuses on the effect of Hall current on an unsteady free convection slip flow of a Casson fluid past an infinite vertical permeable plate in presence of variable suction. The non-linear coupled partial differential equations of the momentum and energy, which control the flow field, are converted into a system of ordinary differential equations using perturbation technique. The resulting equations are solved analytically with the objective of getting non-dimensional velocity and temperature fields. The study has also presented graphically the velocity and temperature profiles for different values of the parameters entering into the problem. Skin friction coefficient and Nusselt number which are of physical interest are sorted out and presented in the form of graphics.

Nonlinear unsteady streaks engendered by the interaction of free-stream vorticity with a compressible boundary layer

The nonlinear response of a compressible boundary layer to unsteady free-stream vortical fluctuations of the convected-gust type is investigated theoretically and numerically. The free-stream Mach number is assumed to be of $O(1)$ and the effects of compressibility, including aerodynamic heating and heat transfer at the wall, are taken into account. Attention is focused on low-frequency perturbations, which induce strong streamwise-elongated components of the boundary-layer disturbances, known as streaks or Klebanoff modes. The amplitude of the disturbances is intense enough for nonlinear interactions to occur within the boundary layer. The generation and nonlinear evolution of the streaks, which acquire an $O(1)$ magnitude, are described on a self-consistent and first-principle basis using the mathematical framework of the nonlinear unsteady compressible boundary-region equations, which are derived herein for the first time. The free-stream flow is studied by including the boundary-layer displacement effect and the solution is matched asymptotically with the boundary-layer flow. The nonlinear interactions inside the boundary layer drive an unsteady two-dimensional flow of acoustic nature in the outer inviscid region through the displacement effect. A close analogy with the flow over a thin oscillating airfoil is exploited to find analytical solutions. This analogy has been widely employed to investigate steady flows over boundary layers, but is considered herein for the first time for unsteady boundary layers. In the subsonic regime the perturbation is felt from the plate in all directions, while at supersonic speeds the disturbance only propagates within the dihedron defined by the Mach line. Numerical computations are performed for carefully chosen parameters that characterize three practical applications: turbomachinery systems, supersonic flight conditions and wind tunnel experiments. The results show that nonlinearity plays a marked stabilizing role on the velocity and temperature streaks, and this is found to be the case for low-disturbance environments such as flight conditions. Increasing the free-stream Mach number inhibits the kinematic fluctuations but enhances the thermal streaks, relative to the free-stream velocity and temperature respectively, and the overall effect of nonlinearity becomes weaker. An abrupt deviation of the nonlinear solution from the linear one is observed in the case pertaining to a supersonic wind tunnel. Large-amplitude thermal streaks and the strong abrupt stabilizing effect of nonlinearity are two new features of supersonic flows. The present study provides an accurate signature of nonlinear streaks in compressible boundary layers, which is indispensable for the secondary instability analysis of unsteady streaky boundary-layer flows.

Viscoelastic fluid flow through an annulus with relaxation, retardation effects and external heat source/sink

Analysis of unsteady hydro-magnetic viscoelastic fluid flow through an annulus (bounded by two infinite co-axial circular cylinders) has been made in presence of radiation, periodic pressure gradient and external heat source/sink. To study the viscoelastic effects, Oldroyd fluid model has been used. Governing partial differential equations are converted into ordinary differential equation and are solved analytically using modified Bessel functions of first kind Iυ(z) and second kind Kυ(z). Effects of relaxation and retardation parameters with other flow parameters are shown in graphically and in tabular form and their effects are seen maximum in the central portion of the annular region.

Numerical analysis of the hydraulic transient response in the presence of surge tanks and relief valves

Water hammer as a critical consequence of unsteadiness may take place in the penstock of the hydroelectric power plants. Hence, the unsteady flow analysis is important to identify undesirable pressure variations and to take preventive actions toward guaranteeing safe operation of the power plant. Chief among these actions are the installation of a surge tank and relief valve, and the transient flow behavior in the presence of protective devices is investigated herein. The method of characteristics is employed to numerically solve the equations governing the transient flow through channels. Also, in order to better resolve the transient behavior, unsteady friction effects have been considered. Validation of the developed computational code is carried out through comparison of the computed transient pressures with those measured at Karun-III Hydropower Plant. According to the results obtained for MONJ Hydropower Station, when only one turbine is in operation, the surge tank decreases the pressure rise within the spiral case and the turbine overspeed by 22% and 6%, respectively. While the percentages associated with employing a proper surge relief valves are accordingly 12% and 14%. This study substantiates how surge relief valves can be used instead of an expensive surge tank to relieve the transient response.

Corrigendum by Simeon Oka, Editor-in-Chief of the Journal Thermal Science requested to replace .pdf file of the paper The effect of variable magnetic field on heat transfer and flow analysis of unsteady squeezing nanofluid flow between parallel plates using Galerkin method by Mohammad Rahimi-Gorji Oveis Pourmehran, Mofid Gorji-Bandpy and Davood Domiri Ganji, Published in the Journal Thermal Science, year 2017,

Due to error of the Editorial staff, unrevised manuscript has been published instead of the REVISED MANUSCRIPT sent by authors after peer review process. The corrected version of this article is printed in this issue on pages pp. 3063-3073<br><br><font color="red"><b> Link to the corrected article <u><a href="http://dx.doi.org/10.2298/TSCI160524180R">10.2298/TSCI160524180R</a></b></u>

Analysis of in-line check valve with respect to the pipeline dynamics

The following study is focused on the flow analysis within the concentric in-line check valve. In-line check valve is part of the pipe and shut off the stream of fluid. In case that backflow occurs on the downstream side, the valve is fully or partially lifted and then abruptly closes. This effect brings undesirable pressure shocks in the entire system. The study therefore deals with the CFD analysis of steady and unsteady flow with respect to velocity and pressure field. Especially unsteady calculation mode reflects the influence of local inertial acceleration acting on the fluid and on the valve. Analysis is complemented by equation of motion of a valve which interacts with the fluid.

Numerical analysis of unsteady 3D flow of Carreau nanofluid with variable thermal conductivity and heat source/sink

Inspired by modern deeds of nanotechnology and nanoscience and their abundant applications in the field of science and engineering, we establish a mathematical relation for unsteady 3D forced convective flow of Carreau nanofluid over a bidirectional stretched surface. Heat transfer phenomena of Carreau nanofluid is inspected through the variable thermal conductivity and heat generation/absorption impact. Furthermore, this research paper presents a more convincing approach for heat and mass transfer phenomenon of nanoliquid by utilizing new mass flux condition. Practically, zero mass flux condition is more adequate because in this approach we assume nanoparticle amends itself accordingly on the boundaries. Now the features of Buongiorno’s relation for Carreau nanofluid can be applied in a more efficient way. An appropriate transformation is vacant to alter the PDEs into ODEs and then tackled numerically by employing bvp4c scheme. The numerous consequence of scheming parameters on the Carreau nanoliquid velocity components, temperature and concentration fields are portrayed graphically and deliberated in detail. The numerical outcomes for local skin friction and the wall temperature gradient for nanoliquid are intended and vacant through tables. The outcomes conveyed here manifest that impact of Brownian motion parameter Nb on the rate of heat transfer for nanoliquids becomes negligible for the recently recommended revised relation. Addationally, for authentication of the present relation, the achieved results are distinguished with earlier research works in specific cases and marvelous agreement has been noted.