Three-dimensional Unsteady Viscous Flow Research Articles

Numerical and Experimental Analysis of Transient Flow Field and Pressure Pulsations of an Axial-Flow Pump Considering the Pump–Pipeline Interaction

The internal flow in a vertical axial-flow pump is a complex unsteady three-dimensional viscous flow. An unstable flow often produces complex flow phenomena such as flow separation, vortices, and secondary reflux, which reduces the operating efficiency of the pump and can endanger safety and stability. In this paper, computational fluid dynamics is used to calculate the flow characteristics in an axial-flow pump using the shear stress transport and curvature correction (SST-CC) model for turbulence modified to account for the rotational curvature. Furthermore, the dependability of the numerical results was confirmed by a test with an actual model of a pump. The transient deviation angle at the impeller inlet of the pump, the stream field attributes in various spanwise parts of the impeller and guide vane, and the velocity distributions at the impeller inlet and outlet were analyzed. The omega method was utilized to recognize the vortex structure inside the guide vane. Moreover, the development of the transient vortex structure inside the guide vane was studied. As the flow rate increased, the scale and turbulent kinetic energy of the vortex structure gradually decreased. The time-domain graph for the impeller inlet is clearly periodic, with three peaks and three troughs in an impeller rotational period. The dominant frequency in the spectrum at each monitoring point was basically the blade frequency, and the secondary dominant frequency was twice the blade frequency.

Transient Behavior of a Prototype Centrifugal Pump with Abrupt Decreasing Flow Rate

Centrifugal pump often operates at different working flow rates to meet engineering requirement. To better reveal the transient behavior of centrifugal pump in the process of decreasing flow rate, the finite volume method (FVM), RNG k-ε turbulence model, sliding mesh technology, and user-defined functions (UDF) were employed to simulate the three-dimensional unsteady viscous incompressible flow in a low-specific-speed centrifugal pump during the abrupt valve-off period. The results show that the differences are very obvious between transient and quasi-steady calculations. The velocity is maximum on the wall of hub and shroud, while the velocity is minimum and uniform distribution at middle positions. The transient flow field lags behind the quasi-steady flow field, which may be related to the reasons; namely, kinetic energy cannot convert pressure energy in time.

Effects of the Advance Ratio on the Evolution of Propeller Wake

This study numerically carried out the propeller open water test (POW) by solving Navier-Stokes equations governing the three-dimensional unsteady incompressible viscous flow with the turbulence closure model of the Κ-ω SST model. Numerical simulations were performed at wide range of advance ratios. A great difference of velocity magnitude between the inner region and the outer region of the slipstream tube forms the thick and large velocity gradient which originates from the propeller tip and develops along the downstream. Eventually, the strong shear layer appears and plays the role of the slipstream boundary. As the advance ratio increases, the vortical structures originated from the propeller tips quickly decay. The contraction of the vortices trace is considerable with decreasing the advance ratio.

A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers.

Numerical prediction of hydrodynamic forces on a moored ship due to a passing ship

The passing ship effect on berthed vessel is a well-known problem and is studied over many years. These interaction effects induce dynamic loads in the mooring system that can exceed the design values and lead to severe accidents. A study has been conducted to analyze the effect of various parameters such as passing ship speed, separation distance, depth to draft ratio and waterway geometry on the hydrodynamic interaction effects between berthed and a passing ship. Numerical simulation for three-dimensional unsteady viscous flow have been conducted using the overset mesh methodology and solving the Reynolds-averaged Navier–Stokes equations with k-ω shear-stress transport turbulence model for various cases, and interaction effect on berthed ship have been calculated. The method recommended in this study is validated by comparing the computational fluid dynamics (numerical) results with existing model scale experiments and mathematical curves from empirical formulas. The hydrodynamic interaction forces are computed for five types of waterway geometries. The magnitude and time histories of the forces and moment on the moored ship for various cases are analyzed to evaluate the effect of various parameters such as waterway geometries and separation distance. The results and conclusions made by this study can give definite guidance on safe maneuvering of a ship passing by a moored ship.

Моделирование трехмерных нестационарных вязких сжимаемых течений на графических картах с помощью алгоритма DiamondTorre

Моделирование трехмерных нестационарных вязких сжимаемых течений на графических картах с помощью алгоритма DiamondTorre

Three-Dimensional Numerical Simulation of Aerodynamic Drag on High-speed Train in Tunnel

The purpose of the paper is to derive variation law of aerodynamic drag introduced by high-speed train passing through a tunnel and to offer guidance for design of high-speed railway longitudinal section and high-speed train head shape. The paper presents a cell-centered finite volume scheme for numerical integration of Navier-Stokes equations for three-dimensional unsteady viscous compressible nonhomentropic flow to simulate the aerodynamic drag introduced by high-speed train passing through a tunnel. The aerodynamic drag curve is analysed and explained in detail in accord with the train positions．

Numerical prediction of hydrodynamic forces on a berthed ship induced by a passing ship in different waterway geometries

An investigation has been conducted to quantify the effect of waterway geometry on the form and magnitude of forces and moment experienced by a berthed ship due to a passing ship. By using the dynamic mesh technique and solving the unsteady RANS equations in conjunction with a RNG k-e turbulence model, numerical simulation of the three-dimensional unsteady viscous flow around a passing ship and a berthed ship in different waterway geometries is conducted, and the hydrodynamic forces and moment acting on the berthed ship are calculated. The proposed method is verified by comparing the numerical results with existing empirical curves and a selection of results from model scale experiments. The calculated interaction forces and moment are presented for six different waterway geometries. The magnitude of the peak values and the form of the forces and moment on the berthed ship for different cases are investigated to assess the effect of the waterway geometry. The results of present study can provide certain guidance on safe maneuvering of a ship passing by a berthed ship.

Numerical Investigation of Transient Flow in a Prototype Centrifugal Pump during Startup Period

AbstractTransient performance of pumps during transient operating periods, such as startup and stopping, has drawn more and more attentions recently due to the growing engineering needs. During the startup period of a pump, the performance parameters such as the flow rate and head would vary significantly in a broad range. Therefore, it is very difficult to accurately specify the unsteady boundary conditions for a pump alone to solve the transient flow in the absence of experimental results. The closed-loop pipe system including a centrifugal pump is built to accomplish the self-coupling calculation. The three-dimensional unsteady incompressible viscous flow inside the passage of the pump during startup period is numerically simulated using the dynamic mesh method. Simulation results show that there are tiny fluctuations in the flow rate even under stable operating conditions and this can be attributed to influence of the rotor–stator interaction. At the very beginning of the startup, the rising speed of the flow rate is lower than that of the rotational speed. It is also found that it is not suitable to predict the transient performance of pumps using the calculation method of quasi-steady flow, especially at the earlier period of the startup.

Adjoint-Based Optimization of Three-Dimensional Flapping-Wing Flows

Optimization of the three-dimensional unsteady viscous flow near a flapping wing in hover is performed using a time-dependent adjoint-based methodology. The sensitivities of a penalized lift coefficient to wing shape and kinematic parameters are computed using a time-dependent discrete-adjoint formulation. The unsteady discrete-adjoint equations required for the calculation of the sensitivity derivatives are integrated backward in time over the entire interval of interest. The gradient of the objective functional obtained using the adjoint formulation is then used to update the values of shape and kinematic design variables. The efficiency of this adjoint-based methodology is demonstrated by optimizing the shape and kinematics of a hovering wing. The numerical results show that the highest improvement in the wing performance is obtained by using combined optimization of the wing shape and kinematics.

Numerical study on hydrodynamic interaction between a berthed ship and a ship passing through a lock

Hydrodynamic interaction between a berthed ship and a passing ship always occurs in a single way lock. This interaction will have significant influences on safe navigation of ships in a lock, and thus the hydrodynamic mechanism behind it should be well understood. In this paper, a numerical study on the hydrodynamic interaction between a berthed ship and a passing ship entering and leaving a single way lock is carried out. By solving the unsteady RANS equations in conjunction with a RNG k−ε turbulence model, numerical simulation of the three-dimensional unsteady viscous flow around the two ships is conducted, and the hydrodynamic interaction is numerically predicted. Dynamic mesh method and sliding interface technique are used to deal with the relative motion between the passing ship and the lock. The numerical results are obtained under different ship speed, water depth, transverse and longitudinal positions of the berthed ship; and the influences of these factors on the ship–ship and ship–lock hydrodynamic interaction are analyzed. This study can provide certain guidance on safe manoeuvring and control of a ship passing through a lock affected by a berthed ship.

프로펠러 회전류에서 작동하는 방향타의 받음각 특성 연구

This study aims at numerically investigating the angle of attack characteristics of the rudder behind a rotating propeller. The rotating propeller of 5 blades and the full spade rudder are placed in the numerical water tunnel with a uniform flow condition to consider propeller-rudder interaction. The turbulence closure model is employed to simulate the three-dimensional unsteady incompressible viscous turbulent flow around the propeller and the rudder. The present numerical method are well verified by comparing with the experimental results. In order to identify the dependence of the angle of attack of the rudder on the rudder angle, a wide range of rudder angles is considered. The present study carried out the quantitative and qualitative analysis of the angle of attack in terms of the pressure distribution, streamlines and the evaluation of the flow incidence, resulting in that the angle of attack increases as we move from the root and the tip to the center of the rudder, regardless of the rudder angle. The distribution of the angle-of-attack along the span is strongly affected by rotating propeller flow and rudder angle. Consequently, the distribution of the angle-of-attack of the oncoming flow against the rudder leading edge plays a role in determination of rudder performance.

Numerical Optimization of Impeller for Backward-Curved Centrifugal Fan by Response Surface Methodology (RSM)

A numerical optimum study on three-dimensional unsteady viscous flow in a centrifugal fan with backward-curved blades was performed. The influence of the inlet angle, the outlet blade angle and blade number on aerodynamic performance of the centrifugal fan was analyzed concerning the whole impeller-volute configuration. Response Surface Methodology (RSM) based on a three-level, three -variable Box-Behnken Design (BBD) was used to evaluate the interactive effects of factors such as inlet blade angle (37°-41°), outlet blade angle (61°-65°) and number of blade (10-14) on the efficiency. The optimum factors deriving via RSM were: inlet blade angle 37°, outlet blade angle 61.7° and blade number 14. The maximum efficiency was 93.7%, under optimum conditions. The method of reliable CFD technique in combination with RSM can be effectively applied to the improvement and experiment design of centrifugal fans.

Transient internal characteristic study of a centrifugal pump during startup process

The transient process of a centrifugal pump existed in a variety of occasions. There were a lot of researches in the external characteristic in startup process and stopping process, but internal characteristics were less observed and studied. Study of the internal flow field had significant meanings. The performance of a pump could be evaluated and improved by revealing the flow field. In the other hand, the prediction of external characteristic was based on the correct analysis of the internal flow. In this paper, theoretical method and numerical simulation were used to study the internal characteristic of a centrifugal pump. The theoretical study showed that the relative flow in an impeller was composed of homogeneous flow and axial vortex flow. The vortex intensity was mainly determined by angular velocity of impeller, flow channel width and blade curvature. In order to get the internal flow field and observe the evolution of transient internal flow in the impeller, Computational Fluid Dynamics(CFD) were used to study the three-dimensional unsteady incompressible viscous flows in a centrifugal pump during starting period. The Dynamic Mesh (DM) method with non-conformal grid boundaries was applied to get the external characteristic and internal flow field. The simulate model included three pumps with different blade numbers and the same blade curvature. The relative velocity vector showed that there was a big axial vortex in impeller channel. At the beginning, the vortex was raised in the pressure side of the impeller outlet and with time went on, it shifted to the middle flow channel of the impeller and the vortex intensity increased. When the speed and flow rate reached a definite value, the influence of the axial vortex began to get smaller. The vortex developed faster when the flow channel got narrower. Due to the evolution of axial vortex, the slip factor during starting period was smaller than that in quasi-steady condition. As a result, transient head was lower than quasi-steady head in startup process.

프로펠러 후류의 총와도 수식모델 연구

This study numerically carried out the propeller open water test(POW) by solving Navier-Stokes equations governing the three-dimensional unsteady incompressible viscous flow with the turbulence closure model of the <TEX>${\kappa}-{\omega}$</TEX> SST model. Numerical simulations are performed at various range of advance ratios. Corresponding to Reynolds numbers of <TEX>$5.89{\times}105{\sim}6.47{\times}105$</TEX> based on free stream velocity and the chord length at 0.7 propeller radius. The present results give a good agreement with those of the experiment. The propeller induced vortical structures have been analyzed by visualizing the resultant vorticity. As the advance ratio increases, the magnitude and length of the resultant vorticity decrease significantly. As the main focus of present study, the numerical model to present the (<TEX>$r-{\theta}$</TEX>) plane-averaged resultant vorticity along the streamwise direction for various advance ratios has been suggested.

Exact Solution of Three-Dimensional Unsteady Stagnation Flow on a Heated Plate

XACT solutions of Navier–Stokes and energy equations regardingtheproblemofstagnation-point flowandheattransfer inthevicinityofa flatplateoracylinderarefoundintheliteraturefor many cases. Fundamental studies in which flows are readily superposed and/or the axisymmetric case were considered include the following papers presented in the literature: two-dimensional stagnation-point flow [1]; three-dimensional stagnation-point flow [2]; and axisymmetric stagnation flow on a circular cylinder [3]. Further exact solutions to the Navier–Stokes equations are obtained by superposition of the uniform shear flow and/or stagnation flow on a body oscillating or rotating in its own plane or cylinder, with or without suction. The examples are: superposition of twodimensional and three-dimensional stagnation-point flows [4]; superposition ofstagnation-point flowon a flatplateoscillating in its own plate, and also consideration of the case where the plate is stationary and the stagnation stream is made to oscillate done [5]; heat Transfer in an axisymmetric stagnation flow on a cylinder [6]; nonsimilar axisymmetric stagnation flow on a moving cylinder [7]; unsteady viscous flow in the vicinity of an axisymmetric stagnationpoint on a cylinder [8]; axisymmetric stagnation flow towards a movingplate[9];axisymmetricstagnation-point flowimpingingona transversely oscillating plate with suction [10]; axisymmetric stagnation-point flowandheattransferofaviscous fluidonamoving cylinder with time-dependent axial velocity and uniform transpiration [11] and also [12–14] can be mentioned. In this study the three-dimensional unsteady viscous stagnation flow and heat transfer in the vicinity of an accelerated flat plate are investigated by solving Navier–Stokes equations in Cartesian coordinate system. The external fluid, along z-direction, with strain rate a impinges on this flat plate while the plate is moving with variable velocity and acceleration along z-direction. A self-similar solution for the Navier–Stokes equations and energy equation is derivedinthisproblem.Areductionoftheseequationsisobtainedby use of these appropriate similarity transformations. The obtained ordinary differential equations are solved using numerical techniques. Velocity and pressure profiles, boundary-layer thickness and surface stress-tensors along with temperature profiles are presented for different values of impinging fluid strain rate, different plate velocities and Prandtl-number parameters for the steady state case.

Numerical Simulation of the Transient Flow in a Centrifugal Pump During Starting Period

Computational fluid dynamics were used to study the three-dimensional unsteady incompressible viscous flows in a centrifugal pump during rapid starting period (≈0.12 s). The rotational speed variation of the field around the impeller was realized by a dynamic slip region method, which combines the dynamic mesh method with nonconformal grid boundaries. In order to avoid introducing errors brought by the externally specified unsteady inlet and outlet boundary conditions, a physical model composed of a pipe system and pump was developed for numerical self-coupling computation. The proposed method makes the computation processes more close to the real conditions. Relations between the instantaneous flow evolutions and the corresponding transient flow-rate, head, efficiency and power were analyzed. Relative velocity comparisons between the transient and the corresponding quasisteady results were discussed. Observations of the formations and evolutions of the primary vortices filled between the startup blades illustrate the features of the transient internal flow. The computational transient performances qualitatively agree with published data, indicating that the present method is capable of solving unsteady flow in a centrifugal pump under transient operations.

Computation of aerodynamic noise of centrifugal fan using large eddy simulation approach, acoustic analogy, and vortex sound theory

Large eddy simulation is applied to solve the unsteady three-dimensional viscous flow in the whole impeller-volute configuration of a centrifugal fan. The results of the simulation are used to predict the impeller-volute interaction and to obtain the unsteady pressure, velocity, and vorticity fluctuations in the impeller and volute casing. The simulation at the design point is carried out with the wall-adapting local eddy-viscosity subgrid-scale model and a sliding mesh technique is applied to consider the impeller-volute interaction. The results show that a strongly unsteady flow field occurs in the impeller and volute casing of the fan, and the flow is characterized with obvious pressure and vorticity fluctuations, especially at the tongue and at the blade wake region. The large pressure fluctuation at the tongue and the large fluctuation of the blade wake vorticity appear as the blade wake is passing the tongue. Acoustic analogy and vortex sound theory are used to compute the radiated dipole and quadrupole sound fields, which are in good agreement with the experiment. The sound results show that the vortex sound theory is convenient for the broadband noise computation, and the dipole sound is much higher than the quadrupole sound. The dipoles, distributed over the volute tongue surface, are the dominant sound source of the fan.

The simulation of 3D unsteady incompressible flows with moving boundaries on unstructured meshes

The development of a computational model for the simulation of three-dimensional unsteady incompressible viscous fluid flows with moving boundaries is presented. The numerical model is based upon the solution of the Navier–Stokes equations on unstructured meshes using the artificial compressibility approach. An ALE formulation is adopted and the equations are discretized using a cell vertex finite volume method. The formulation ensures the satisfaction of the geometric conservation law when the mesh is allowed to move. An implicit time discretization is adopted and a dual time approach is employed. Explicit relaxation is used for the sub-iterations, with multigrid acceleration. For moving geometries, the mesh is deformed by adopting a spring analogy, combined with a wall distance function approach. The numerical procedure is validated on a standard problem and is then used for the simulation of flow over a flexible fish-like body.

Numerical Simulation of Three Dimensional Transient Aerodynamic Characteristics of Two Crossing Vehicles

The flow around the crossing vehicles is one kind of three-dimensional unsteady viscous incompressible flow. The finite volume method and the fully implicit scheme were adopted to discretize the Navier-Stokes equations of this flow in space and time, respectively, and the solving procedure of velocity and pressure in the flow field is based on PISO algorithm. The moving mesh strategy was presented to realize the relative movement of two vehicles with the time. The numerical simulation obtained the transient characteristics of aerodynamic force coefficients: the aerodynamic force coefficients vary abruptly and dramatically like a cosine curve at a certain period of time while vehicles are moving oppositely and crossing, and the coefficients of side force vary more severely, which deteriorates the moving stability of the high speed vehicles. The conclusions of the transient aerodynamic characteristics drawn from the simulation can provide references for the drivers or an intelligent driving system to properly steer and handle the vehicles in the crossing condition.