Discrete Optimization on Unsteady Pressure Fluctuation of a Centrifugal Pump Using ANN and Modified GA

Pressure fluctuation due to rotor-stator interaction in turbomachinery is unavoidable,inducing strong vibration in the equipment and shortening its lifecycle.The investigation of optimization methods for an industrial centrifugal pump was carried out to reduce the intensity of pressure fluctuation to extend the lifecycle of these devices.Considering the time-consuming transient simulation of unsteady pressure,a novel optimization strategy was proposed by discretizing design variables and genetic algorithm.Four highly related design parameters were chosen,and 40 transient sample cases were generated and simulated using an automatic program.70%of them were used for training the surrogate model,and the others were for verifying the accuracy of the surrogate model.Furthermore,a modified discrete genetic algorithm(MDGA)was proposed to reduce the optimization cost owing to transient numerical simulation.For the benchmark test,the proposed MDGA showed a great advantage over the original genetic algorithm regarding searching speed and effectively dealt with the discrete variables by dramatically increasing the convergence rate.After optimization,the performance and stability of the inline pump were improved.The efficiency increased by more than 2.2%,and the pressure fluctuation intensity decreased by more than 20%under design condition.This research proposed an optimization method for reducing discrete transient characteristics in centrifugal pumps.

Meshfree-based physics-informed neural networks for the unsteady Oseen equations

We propose the meshfree-based physics-informed neural networks for solving the unsteady Oseen equations.Firstly,based on the ideas of meshfree and small sample learning,we only randomly select a small number of spatiotemporal points to train the neural network instead of forming a mesh.Specifically,we optimize the neural network by minimizing the loss function to satisfy the differential operators,initial condition and boundary condition.Then,we prove the convergence of the loss function and the convergence of the neural network.In addition,the feasibility and effectiveness of the method are verified by the results of numerical experiments,and the theoretical derivation is verified by the relative error between the neural network solution and the analytical solution.

A dynamic-mode-decomposition-based acceleration method for unsteady adjoint equations at low Reynolds numbers

The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic op-timization.In this letter,the solution of unsteady adjoint equations is accelerated by dynamic mode decomposi-tion(DMD).The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system.Thereafter,DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching.First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step.Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example,the efficiency of solving unsteady adjoint equations is significantly improved.Re-sults show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics,and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors,which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.

Numerical Study by Imposing the Finite Difference Method for Unsteady Casson Fluid Flow with Heat Flux

This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip velocity, thermal radiation conditions, and heat flux. The investigation is conducted employing a robust numerical method that accounts for the impact of thermal radiation. This category of fluid is apt for characterizing the movement of blood within an industrial artery, where the flow can be regulated by a material designed to manage it. The resolution of the ensuing system of ordinary differential equations (ODEs), representing the described problem, is accomplished through the application of the finite difference method. The examination of flow and heat transfer characteristics, including aspects such as unsteadiness, radiation parameter, slip velocity, Casson parameter, and Prandtl number, is explored and visually presented through tables and graphs to illustrate their impact. On the stretching sheet, calculations, and descriptions of the local skin-friction coefficient and the local Nusselt number are conducted. In conclusion, the findings indicate that the proposed method serves as a straightforward and efficient tool for exploring the solutions of fluid models of this kind.

Mechanism of unsteady aerodynamic heating with sudden change in surface temperature

The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new inflexion near the wall occurs in the profile of the thermal boundary layer. This is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, meaning that, in a long-term aerodynamic heating process considering only unsteady surface temperature, the unsteady characteristics of the flow can be ignored, and the traditional quasi-steady aerodynamic heating prediction methods are still valid.

Unsteady Turbulent Simulation and Pressure Fluctuation Analysis for Centrifugal Pumps

The pressure fluctuation in the flow passage of both impeller and casing is addressed on design condition. The initial conditions for the unsteady turbulent simulation are resulted from the steady calculations, and the three dimensional unsteady turbulent simulation concerning the rotor-stator interaction is executed by a Navier-Stoke solver embedded with k -ε turbulence model and with appropriate moving interface boundary conditions. Detecting points are distributed in the flow passage in different radial and circumferential positions to capture the static pressure fluctuation character for one cycle of the impeller. The time-domain spectrums show that the static pressure curves are periodic and have five peaks and five valleys. With the radius increasing, the pressure fluctuation peak-to-peak values in the impeller are increasing, and reach the maximum value on the interface. In the casing flow passage, those values are about 7% of local static pressure except some ones near the tongue. The values become decreasingly in the diffuser pipe. The frequency spectrums transformed by fast Fourier transform （FFT） show that the dominant frequency is approximate with the blade passing frequency, and the pressure fluctuations in impeller passage have high frequency content while those in casing ones have no such information.

UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

Studies of the unsteady supersonic base flows around three afterbodies

Unsteady supersonic base flows around three afterbodies, cylindrical （Cy）, boattailed （BT） and three-step （MS）, are investigated in this paper. Reynolds-averaged Navier-Stokes （RANS） and two RANS/LES （large-eddy simulation） hybrid methods, detached eddy simulation （DES） and delayed-DES （DDES）, are used to predict the base flow characteristics around the baseline Cy afterbody. All the RANS and hybrid methods are based on the two-equation SST （shear-stress transport） model with compressible corrections （CC）. According to the comparison of measurements, both DES and DDES can produce more satisfactory results than RANS. RANS can only present the ＂stable＂ flow pat- terns, while the hybrid methods can demonstrate unsteady flow structures. DDES and DES results are little different from one another although the latter exhibits better agreement with the experiment. DES is taken to investigate the 5° BT and three-step afterbodies. The mean flow data and the instantaneous turbulent coherent structures are compared against available measurements.

Unsteady Flow and Structural Behaviors of Centrifugal Pump under Cavitation Conditions

Cavitation has a significant e ect on the flow fields and structural behaviors of a centrifugal pump. In this study, the unsteady flow and structural behaviors of a centrifugal pump are investigated numerically under di erent cavitation conditions. A strong two-way coupling fluid-structure interaction simulation is applied to obtain interior views of the e ects of cavitating bubbles on the flow and structural dynamics of a pump. The renormalization-group k-ε turbulence model and the Zwart–Gerbe–Belamri cavitation model are solved for the fluid side, while a transient structural dynamic analysis is employed for the structure side. The di erent cavitation states are mapped in the head-net positive suction head(H-NPSH) curves and flow field features inside the impeller are fully revealed. Results indicate that cavitating bubbles grow and expand rapidly with decreasing NPSH. In addition, the pressure fluctuations, both in the impeller and volute, are quantitatively analyzed and associated with the cavitation states. It is shown that influence of the cavitation on the flow field is critical, specifically in the super-cavitation state. The e ect of cavitation on the unsteady radial force and blade loads is also discussed. The results indicate that the averaged radial force increased from 8.5 N to 54.4 N in the transition progress from an onset cavitation state to a super-cavitation state. Furthermore, the structural behaviors, including blade deformation, stress, and natural frequencies, corresponding to the cavitation states are discussed. A large volume of cavitating bubbles weakens the fluid forces on the blade and decreases the natural frequencies of the rotor system. This study could enhance the understanding of the e ects of cavitation on pump flow and structural behaviors.

Unsteady boundary layer flow and heat transfer over an exponentially shrinking sheet with suction in a copper-water nanofluid

An analysis of unsteady boundary layer flow and heat transfer over an exponentially shrinking porous sheet filled with a copper-water nanofluid is presented.Water is treated as a base fluid.In the investigation,non-uniform mass suction through the porous sheet is considered.Using Keller-box method the transformed equations are solved numerically.The results of skin friction coefficient,the local Nusselt number as well as the velocity and temperature profiles are presented for different flow parameters.The results showed that the dual non-similar solutions exist only when certain amount of mass suction is applied through the porous sheet for various unsteady parameters and nanoparticle volume fractions.The ranges of suction where dual non-similar solution exists,become larger when values of unsteady parameter as well as nanoparticle volume fraction increase.So,due to unsteadiness of flow dynamics and the presence of nanoparticles in flow field,the requirement of mass suction for existence of solution of boundary layer flow past an exponentially shrinking sheet is less.Furthermore,the velocity boundary layer thickness decreases and thermal boundary layer thickness increases with increasing of nanoparticle volume fraction in both non-similar solutions.Whereas,for stronger mass suction,the velocity boundary layer thickness becomes thinner for the first solution and the effect is opposite in the case of second solution.The temperature inside the boundary layer increases with nanoparticle volume fraction and decreases with mass suction.So,for the unsteadiness and for the presence of nanoparticles,the flow separation is delayed to some extent.

Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders

The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.

Numerical simulation of unsteady interaction of centrifugal impeller with its diffuser using Lagrangian discrete vortex method

In this study, an advanced Lagrangian vortex- boundary element method is applied to simulate the unsteady impeller-diffuser interactions in a diffuser pump not only for design but also for off-design considerations. In velocity calculations based on the Biot-Savart law we do not have to grid large portions of the flow field and the calculation points are concentrated in the regions where vorticity is present. Lagrangian representation of the evolving vorticity field is well suited to moving boundaries. An integral pressure equation shows that the pressure distribution can be estimated directly from the instantaneous velocity and vorticity field. The numerical results are compared with the experimental data and the comparisons show that the method used in this study can provide us insight into the complicated unsteady impeller-diffuser interaction phenomena in a diffuser pump.

Unsteady Cavitating Flow around a Hydrofoil Simulated Using the Partially-Averaged Navier-Stokes Model

Numerical simulations of unsteady cavitating flow around a NACA66-mod hydrofoil were performed using the partially-averaged Navier-Stokes method with different values of the resolution control parameters (f k =1.0-0.2,fε =1).With decreasing fk,the predicted cavitating flow becomes unsteady as the time-averaged turbulent viscosity at the rear part of the attached cavity is gradually reduced.For fk =0.9 and 0.8,the cavity becomes unstable and its length dramatically expands and shrinks,but the calculation fails to predict the vapor cloud shedding behavior observed experimentally.With smaller fk less than 0.7,the cloud shedding behavior is simulated numerically and the predicted cavity shedding frequency increases.With fk =0.2,the whole cavitating flow evolution can be reasonably reproduced including the cavity growth/destabilization observed previously.The reentrant flow along the suction surface of the hydrofoil is the main trigger to cause the vapor cloud shedding.The wall pressure along the hydrofoil surface oscillates greatly due to the dynamic cavity shedding.Comparing the simulations and experiments,it is confirmed that for the PANS method,resolution control parameters of fk =0.2and fε =1 are recommended for numerical simulations of unsteady cavitating flows.Thus,the present study shows that the PANS method is an effective approach for predicting unsteady cavitating flow over hydrofoils.

Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight

Aerodynamic forces and power requirements in forward flight in a bumblebee （Bombus terrestris） were studied using the method of computational fluid dynamics. Actual wing kinematic data of free flight were used in the study （the speed ranges from 0 m/s to 4.5 m/s; advance ratio ranges from 0-0.66）. The bumblebee employs the delayed stall mechanism and the fast pitching-up rotation mechanism to produce vertical force and thrust. The leading-edge vortex does not shed in the translatory phase of the half-strokes and is much more concentrated than that of the fruit fly in a previous study. At hovering and low-speed flight, the vertical force is produced by both the half-strokes and is contributed by wing lift; at medium and high speeds, the vertical force is mainly produced during the downstroke and is contributed by both wing lift and wing drag. At all speeds the thrust is mainly produced in the upstroke and is contributed by wing drag. The power requirement at low to medium speeds is not very different from that of hovering and is relatively large at the highest speed （advance ratio 0.66）, i.e. the power curve is Jshaped. Except at the highest flight speed, storing energy elastically can save power up to 20%-30%. At the highest speed, because of the large increase of aerodynamic torque and the slight decrease of inertial torque （due to the smaller stroke amplitude and stroke frequency used）, the power requirement is dominated by aerodynamic power and the effect of elastic storage of energy on power requirement is limited.

Analysis of Unsteady Flow over Offshore Wind Turbines 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.

An application of interacting shear flows theory: exact solution for unsteady oblique stagnation point flow

An analytical solution of the governing equations of the interacting shear flows for unsteady oblique stagnation point flow is obtained. It has the same form as that of the exact solution obtained from the complete NS equations and physical analysis and relevant discussions are then presented.

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1:code development and deterministic correlation analysis

The average-passage equation system （APES） provides a rigorous mathematical framework for account- ing for the unsteady blade row interaction through multi- stage compressors in steady state environment by introduc- ing deterministic correlations （DC） that need to be modeled to close the equation system. The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 1 of this two-part paper, firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investi- gate the APES technique. Then steady and unsteady simu- lations are conducted in a transonic compressor stage. The results from both simulations are compared to highlight the significance of the unsteady interactions. Furthermore, the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial cor- relations （SC）. Lastly, steady and time-averaging （employing APES with DC） simulations for the downstream stator alone are conducted employing DC derived from the unsteady re- suits. The results from steady and time-averaging simula- tions are compared with the time-averaged unsteady results. The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.

Study of modeling unsteady blade row interaction in a transonic compressor stage part 2:influence of deterministic correlations on time-averaged flow prediction

The average-passage equation system （APES） provides a rigorous mathematical framework for account- ing for the unsteady blade row interaction through multistage compressors in steady state environment by introducing de- terministic correlations （DC） that need to be modeled to close the equation system. The primary purpose of this study was to provide insight into the DC characteristics and the in- fluence of DC on the time-averaged flow field of the APES. In Part 2 of this two-part paper, the influence of DC on the time-averaged flow field was systematically studied; Several time-averaging computations boundary conditions and DC were conducted with various for the downstream stator in a transonic compressor stage, by employing the CFD solver developed in Part 1 of this two-part paper. These results were compared with the time-averaged unsteady flow field and the steady one. The study indicat;d that the circumferential- averaged DC can take into account major part of the unsteady effects on spanwise redistribution of flow fields in compres- sors. Furthermore, it demonstrated that both deterministic stresses and deterministic enthalpy fluxes are necessary to reproduce the time-averaged flow field.

Slip Effects on an Unsteady Boundary Layer Stagnation-Point Flow and Heat Transfer towards a Stretching Sheet

An analysis is presented for an unsteady boundary layer stagnation-point flow of a Newtonian fluid and the heat transfer towards a stretching sheet taking non-conventional partial slip conditions at the sheet.The self-similar equations are obtained using similarity transformations and solved numerically by the shooting method.Effects of the parameters involved in the equations,especially velocity slip and thermal slip parameters on the velocity and temperature profiles,are analyzed extensively.It is revealed that due to the velocity and thermal slip parameters,the rate of heat transfer from the sheet and the wall skin friction change significantly.