An Exact Periodic Solution of a Hydromagnetic Flow in a Horizontal Channel

1988 ◽  
Vol 55 (4) ◽  
pp. 981-983 ◽  
Author(s):  
K. Vajravelu
Keyword(s):  
Exact Solution ◽  
Periodic Solution ◽  
Flow Field ◽  
Unsteady Flow ◽  
Incompressible Fluid ◽  
Approximate Solutions ◽  
The Other ◽  
Hydromagnetic Flow ◽  
Mean Velocity ◽  
Approximate Form

An exact periodic solution for the hydromagnetic unsteady flow of an incompressible fluid with constant properties is obtained. The hydrodynamic (HD) and the hydromagnetic (HM) cases are studied. The flow field here is a generalization of the well-known Couette flow, in which one wall is at rest and the other wall oscillates in its own plane about a constant mean velocity. In order to have some suggestions about the approximate solutions, the exact solution is compared with its own approximate form.

An Exact Periodic Solution of a Hydromagnetic Flow of an Oldroyd Fluid in a Channel

1999 ◽  
Vol 66 (4) ◽  
pp. 974-977 ◽  
Author(s):  
R. N. Ray ◽  
A. Samad ◽  
T. K. Chaudhury
Keyword(s):  
Periodic Solution ◽  
Unsteady Flow ◽  
Velocity Gradient ◽  
Separation Of Variables ◽  
The Other ◽  
Parallel Plates ◽  
Hydromagnetic Flow ◽  
Mean Velocity ◽  
Oldroyd Fluid ◽  
Viscoelastic Parameters

The unsteady flow of a conducting Oldroyd fluid between two parallel plates, one of which is at rest and the other oscillating in its own plane with a constant mean velocity, has been investigated. Using separation of variables an exact periodic solution for the problem is obtained. Effects of viscoelastic parameters on velocity gradient, skin friction amplitude, and phase angle of the flow are discussed with graphs.

Pulse Propagation in Inhomogeneous Media

1974 ◽  
Vol 41 (4) ◽  
pp. 1057-1062 ◽  
Author(s):  
D. B. Longcope ◽  
C. R. Steele
Keyword(s):  
Exact Solution ◽  
Opposite Direction ◽  
Wave Speed ◽  
Pulse Propagation ◽  
Characteristic Length ◽  
Pulse Length ◽  
Approximate Solutions ◽  
The Other ◽  
One Dimensional ◽  
Analytic Wave

Approximate solutions are developed for one-dimensional pulse propagation in a medium with an analytic wave speed when the ratio ε of the pulse length to a characteristic length of the wave speed variation is small. The solutions describe an 0(1) transmitted pulse, given by the WKB solution, and an 0(ε) reflection which may progress in the opposite direction. Two approximations for the reflection are given, one in terms of explicit integrals and the other, which may be uniformly valid, by a combination of explicit integrals and a slowly varying numerical term. Comparisons with the exact solution in several examples show the usefulness of the approximate solutions.

An exact periodic solution of the energy equation

1971 ◽  
Vol 50 (4) ◽  
pp. 657-668 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Periodic Solution ◽  
Temperature Field ◽  
Couette Flow ◽  
Energy Equation ◽  
Second Harmonic ◽  
Plate Boundary ◽  
Approximate Solutions ◽  
Mean Velocity ◽  
Mean Temperature ◽  
Layer Flow

An exact periodic solution of the unsteady energy equation for an incompressible fluid with constant properties is derived to illustrate the effect of an oscillation through the viscous dissipation on a temperature field. The flow field used here is a generalization of the well-known Couette flow solution of steady flow, in which one wall is at rest and the other wall oscillates in its own plane about a constant mean velocity. The solution is subject to two boundary conditions that correspond to the heat-transfer and thermometer problems. In order to have some suggestions about the approximate solutions, the solution is compared with its own approximate form. The temperature field consists of a time-mean, first and second harmonic fluctuation. The time-mean temperature profiles show the large influence of oscillation. The time-mean heat flux into or the time-mean temperature of the oscillating wall increases with frequency, and is ultimately proportional to the square root of the frequency. In § 4 the present exact solution of the Couette flow is compared with the formerly obtained approximate solution of the flat plate boundary-layer flow in terms of the wall characteristic values at high frequencies.

scholarly journals Numerical Study of the Unsteady Flow Characteristics of a Jet Centrifugal Pump under Multiple Conditions

Processes ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 786
Author(s):  
Rong Guo ◽  
Rennian Li ◽  
Renhui Zhang ◽  
Wei Han
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Centrifugal Pump ◽  
Temporal Evolution ◽  
Guide Vane ◽  
Flow Characteristics ◽  
The Other ◽  
Flow Passage ◽  
Evolution Laws ◽  
Multiple Conditions

To study the reasons for the low efficiency of jet centrifugal pumps (JCPs) and the mechanism of unsteady flow characteristics under multiple conditions, taking a JET750G1 JCP as the object, three-dimensional steady and unsteady numerical calculations of the model pump were carried out using the k–ω turbulence model. The transient fluctuation characteristics of the flow field in the major flow passage components and the spatial and temporal evolution laws of vortices in the rotor–stator cascades were analyzed. The accuracy of the numerical method was verified by experiments. The results show that there are various scales of flow distortion phenomena in the chamber of the JCP, such as eddies, blockage of the flow passage, recirculation, secondary flow, and circulation, which not only cause great hydraulic loss, but also destroy the flow stability, symmetry, and balance in the other flow passage components. This is an important reason for the obviously lower efficiency of a JCP compared to a general centrifugal pump. The spatial and temporal evolution laws of vortices in the rotor–stator cascades are mainly related to the relative positions of the impeller blades and guide vane blades. The formation mechanism of the unsteady flow field fluctuation characteristics of JCPs is mainly related to the number of blades in the rotor–stator cascades and the operation parameters of the pump. The fluctuation intensity of the flow field inside the impeller and guide vane is obviously greater than that in the other flow areas, reflecting that the rotor–stator interaction is the decisive factor affecting the unsteady flow characteristics of a JCP under multiple conditions.

scholarly journals Exact Solution for Unsteady Flow of Viscous Incompressible Fluid Over a Suddenly Accelerated Flat Plate (Stokes' First Problem) Using Laplace Transforms

2018 ◽  
Vol 7 (3.6) ◽  
pp. 267
Author(s):  
Spainborlang Kharchandy ◽  
. .
Keyword(s):  
Exact Solution ◽  
Unsteady Flow ◽  
Incompressible Fluid ◽  
Flat Plate ◽  
Stokes Equation ◽  
Viscous Incompressible Fluid ◽  
Laplace Transforms ◽  
Simple Approach ◽  
Navier Stokes ◽  
Navier Stokes Equation

With the Navier-Stokes Equation in Cartesian form (in absence of body forces), Laplace Transforms provides a simple approach towards solving the unsteady flow of a viscous incompressible fluid over a suddenly accelerated flat plate. On comparing the results between  Laplace Transforms and similarity methods, it reveals that Laplace Transforms is simple and effective.

Unsteady Flow Field in the Wake of an Airfoil

2009 ◽  
Author(s):  
Hamed Sadeghi ◽  
Mahmoud Mani
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Incidence Angle ◽  
Oscillation Amplitude ◽  
Velocity Profiles ◽  
Instantaneous Velocity ◽  
Mean Velocity ◽  
Velocity Defect ◽  
Incidence Data ◽  
Reduced Frequency

An experimental investigation was carried out to study the unsteady flow field behind a sinusoidally pitching airfoil at reduced frequencies 0.091, 0.182 and 0.273. Streamwise instantaneous velocity and streamwise mean velocity in the wake were measured by hot-wire anemometer at downstream distance from trailing edge of 0.25 chord. To assess the effect of mean incidence, data were taken at mean incidence angles of 0, 2.5 and 5 degrees. In all cases, the oscillation amplitude was set at 8 degree, and the Reynolds number, based on the chord length, was 50000. It is found that the mean incidence angle and reduced frequency have important influences on the instantaneous velocity profiles. As reduced frequency increases, more uniformity and stability in the wake are observed. When mean incidence angle is larger, more variations on thickness of profiles and velocity defect are found. Furthermore, mean velocity profiles and estimations of the momentum deficit coefficients are obtained. The results show that with increasing mean incidence, the velocity defect and momentum deficit increase. Instead, the higher reduced frequency decreases the momentum deficit and wake thickness.

On the Rigid-Lid Hypothesis Application to the Flow Simulation of Step-Feed A/O Process

2014 ◽  
Vol 886 ◽  
pp. 319-322
Author(s):  
Shen Zhao ◽  
Xue Yi You ◽  
Sheng Jun Liu ◽  
Yu Huang ◽  
Feng Shi ◽  
...  
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Velocity Distribution ◽  
Flow Simulation ◽  
The Other ◽  
Surface Model ◽  
Mean Velocity ◽  
Field Simulation ◽  
The Mean ◽  
Free Surface Model

The feasibility of the rigid-lip hypothesis was studied in the flow field simulation of the reaction tank in the step-feed A/O process. Two models were built. One model applied the rigid-lip hypothesis was called as rigid-lid model and the other was called free surface model. The results showed that the velocity distribution of the rigid-lid model is basically consistent with that of the free-surface model. On the vertical monitor sections, the error of the mean velocity between the two models is less than 8%. The results showed that the much less expensive rigid-lid model is applicable to simulate the flow field of reaction tank.

Study of Near-Stall Flow Behavior in a Modern Transonic Fan With Compound Sweep

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
Chunill Hah ◽  
Hyoun-Woo Shin
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Flow Structure ◽  
Flow Behavior ◽  
Pressure Rise ◽  
Tip Clearance ◽  
The Other ◽  
Other Hand ◽  
Transonic Fan ◽  
Tip Clearance Vortex

Detailed flow behavior in a modern transonic fan with a compound sweep is investigated in this paper. Both unsteady Reynolds-averaged Navier-Stokes (URANS) and large eddy simulation (LES) methods are applied to investigate the flow field over a wide operating range. The calculated flow fields are compared with the data from an array of high-frequency response pressure transducers embedded in the fan casing. The current study shows that a relatively fine computational grid is required to resolve the flow field adequately and to calculate the pressure rise across the fan correctly. The calculated flow field shows detailed flow structure near the fan rotor tip region. Due to the introduction of compound sweep toward the rotor tip, the flow structure at the rotor tip is much more stable compared to that of the conventional blade design. The passage shock stays very close to the leading edge at the rotor tip even at the throttle limit. On the other hand, the passage shock becomes stronger and detaches earlier from the blade passage at the radius where the blade sweep is in the opposite direction. The interaction between the tip clearance vortex and the passage shock becomes intense as the fan operates toward the stall limit, and tip clearance vortex breakdown occurs at near-stall operation. URANS calculates the time-averaged flow field fairly well. Details of measured rms static pressure are not calculated with sufficient accuracy with URANS. On the other hand, LES calculates details of the measured unsteady flow features in the current transonic fan with compound sweep fairly well and reveals the flow mechanism behind the measured unsteady flow field.

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

Modal characteristics and fluid–structure interaction vibration response of submerged impeller

2021 ◽  
pp. 107754632110036
Author(s):  
Shihui Huo ◽  
Hong Huang ◽  
Daoqiong Huang ◽  
Zhanyi Liu ◽  
Hui Chen
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Damping Ratio ◽  
Pure Water ◽  
Vibration Response ◽  
Modal Identification ◽  
Liquid Oxygen ◽  
Modal Characteristics ◽  
Oxygen Pump ◽  
Turbo Pump

Turbo pump is one of the elements with the most complex flow of liquid rocket engine, and as an important component of turbo pump, an impeller is the weak point affecting its reliability. In this study, a noncontact modal characteristic identification technique was proposed for the liquid oxygen pump impeller. Modal characteristics of the impeller under three different submerged media, air, pure water, and brine with same density as liquid oxygen, were tested based on the noncontact modal identification technology. Submersion state directly affects the modal frequencies and damping ratio. The transient vibration response characteristics of the impeller excited by the unsteady flow field was achieved combining with unsteady flow field analysis and transient dynamic analysis in the whole flow passage of the liquid oxygen pump. Vibration responses at different positions of the impeller show 10X and 20X frequencies, and the amplitude at the root of short blade is significant, which needs to be paid more attention in structural design and fatigue evaluation.

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