scholarly journals Viscous fluid flow between plane walls in presence of temperature gradient

2021 ◽  
pp. 26-38
Author(s):  
Алексей Олегович Сыромясов ◽  
Татьяна Вячеславовна Меньшакова
Keyword(s):  
Temperature Gradient ◽  
Viscous Fluid ◽  
Fluid Velocity ◽  
Asymptotic Methods ◽  
Temperature Drop ◽  
Fluid Viscosity ◽  
Slow Flow ◽  
First Order ◽  
Order Polynomial ◽  
Isothermal Case

В статье изучается медленный поток вязкой несжимаемой жидкости, ограниченной двумя параллельными плоскостями. Течение вызвано либо движением одной плоскости относительно другой, либо перепадом давления вдоль двух неподвижных плоскостей. Предполагается, что вязкость жидкости есть многочлен первой степени от температуры, а в рассматриваемом объеме поддерживается постоянный градиент этой величины. Это приводит к возмущению потока по сравнению с изотермическим случаем. Асимптотическими методами исследована зависимость возникающих искажений от типа потока и взаимной ориентации потока и градиента температуры. При этом перепад температуры на расстоянии, равном зазору между плоскостями, считается малым. Показано, что эти искажения могут вноситься как в скорость, так и в давление жидкости. В последнем случае при наличии в жидкости взвеси возможно возникновение дополнительной подъемной силы или силы тяги, действующей на инородные частицы. Slow flow of incompressible viscous fluid confined by two parallel planes is studied in the paper. The flow is caused either by motion of one plane with respect to another or by pressure drop along the planes. It is supposed that fluid viscosity is the first-order polynomial of temperature and that its gradient is constant in the entire domain under study. These two reasons cause the flow to be disturbed (compared with isothermal case). Dependence of these disturbances on the type of flow and on the orientation of temperature gradient with respect to the flow is investigated by asymptotic methods. Temperature drop on distances equal to the gap between planes is supposed to be small during the investigation. It is shown that both fluid velocity and pressure may be disturbed. In the last case additional lift or drag force may act on the alien particles suspended in the fluid (if it contains any).

Statistical method of steepest improvement of response

2018 ◽  
Vol 84 (11) ◽  
pp. 74-87
Author(s):  
V. B. Bokov
Keyword(s):  
Statistical Method ◽  
Linear Model ◽  
Response Prediction ◽  
Initial Experiment ◽  
First Order ◽  
Prediction Response ◽  
Conditional Extremum ◽  
Order Polynomial ◽  
Limiting Values

A new statistical method for response steepest improvement is proposed. This method is based on an initial experiment performed on two-level factorial design and first-order statistical linear model with coded numerical factors and response variables. The factors for the runs of response steepest improvement are estimated from the data of initial experiment and determination of the conditional extremum. Confidence intervals are determined for those factors. The first-order polynomial response function fitted to the data of the initial experiment makes it possible to predict the response of the runs for response steepest improvement. The linear model of the response prediction, as well as the results of the estimation of the parameters of the linear model for the initial experiment and factors for the experiments of the steepest improvement of the response, are used when finding prediction response intervals in these experiments. Kknowledge of the prediction response intervals in the runs of steepest improvement of the response makes it possible to detect the results beyond their limits and to find the limiting values of the factors for which further runs of response steepest improvement become ineffective and a new initial experiment must be carried out.

scholarly journals Thematic Maps for the Variation of Bearing Capacity of Soil Using SPTs and MATLAB

Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 329
Author(s):  
Mahdi O. Karkush ◽  
Mahmood D. Ahmed ◽  
Ammar Abdul-Hassan Sheikha ◽  
Ayad Al-Rumaithi
Keyword(s):  
Bearing Capacity ◽  
Mean Squared Error ◽  
Ground Level ◽  
The Other ◽  
Thematic Maps ◽  
First Order ◽  
Squared Error ◽  
Order Polynomial ◽  
Interpolation Polynomials ◽  
Penetration Tests

The current study involves placing 135 boreholes drilled to a depth of 10 m below the existing ground level. Three standard penetration tests (SPT) are performed at depths of 1.5, 6, and 9.5 m for each borehole. To produce thematic maps with coordinates and depths for the bearing capacity variation of the soil, a numerical analysis was conducted using MATLAB software. Despite several-order interpolation polynomials being used to estimate the bearing capacity of soil, the first-order polynomial was the best among the other trials due to its simplicity and fast calculations. Additionally, the root mean squared error (RMSE) was almost the same for the all of the tried models. The results of the study can be summarized by the production of thematic maps showing the variation of the bearing capacity of the soil over the whole area of Al-Basrah city correlated with several depths. The bearing capacity of soil obtained from the suggested first-order polynomial matches well with those calculated from the results of SPTs with a deviation of ±30% at a 95% confidence interval.

Experiments and mechanistic modeling of viscosity effect on a multistage ESP performance under viscous fluid flow

2021 ◽  
pp. 095765092110149
Author(s):  
Yi Shi ◽  
Jianjun Zhu ◽  
Haoyu Wang ◽  
Haiwen Zhu ◽  
Jiecheng Zhang ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Prediction Error ◽  
Flow Direction ◽  
Fluid Viscosity ◽  
Oil Viscosity ◽  
Viscous Fluid Flow ◽  
Viscosity Effect ◽  
High Production Rate ◽  
Pump Head

Assembled in series with multistage, Electrical Submersible Pumps (ESP) are widely used in offshore petroleum production due to the high production rate and efficiency. The hydraulic performance of ESPs is subjected to the fluid viscosity. High oil viscosity leads to the degradation of ESP boosting pressure compared to the catalog curves under water flow. In this paper, the influence of fluid viscosity on the performance of a 14-stage radial-type ESP under varying operational conditions, e.g. rotational speeds 1800–3500 r/min, viscosities 25–520 cP, was investigated. Numerical simulations were conducted on the same ESP model using a commercial Computational Fluid Dynamics (CFD) software. The simulated average pump head is comparable to the corresponding experimental data under different viscosities and rotational speeds with less than ±20% prediction error. A mechanistic model accounting for the viscosity effect on ESP boosting pressure is proposed based on the Euler head in a centrifugal pump. A conceptual best-match flowrate QBM is introduced, at which the impeller outlet flow direction matches the designed flow direction. The recirculation losses caused by the mismatch of velocity triangles and other head losses resulted from the flow direction change, friction loss and leakage flow etc., are included in the model. The comparison of model predicted pump head versus experimental measurements under viscous fluid flow conditions demonstrates good agreement. The overall prediction error is less than ±10%.

Non-Isothermal Peristaltic Flow of Newtonian Fluids in a Circular Tube

2009 ◽  
Author(s):  
M. S. Yun ◽  
B. P. Huynh
Keyword(s):  
Reynolds Number ◽  
Flow Pattern ◽  
Circular Tube ◽  
Pressure Change ◽  
Peristaltic Flow ◽  
Isothermal Flow ◽  
Newtonian Fluids ◽  
Fluid Viscosity ◽  
Fluid Properties ◽  
Isothermal Case

Non-isothermal peristaltic flow of Newtonian fluids in a circular tube is investigated numerically, using a commercial Computational Fluid Dynamics (CFD) software package. Simulation is performed over a range of Reynolds-number values, up to 1000. Temperature affects the flow field via fluid viscosity, which is assumed to decrease exponentially with temperature. Other fluid properties are assumed to be constant, and are similar to those of an oil. Allowing for temperature effects alters significantly the flow pattern and reduces pressure change. In the crest region, recirculation appears in non-isothermal flow at a much smaller Reynolds number Re than in isothermal flow. Influence of the Reynolds number itself is also reduced significantly, such that the flow pattern changes very little with increasing Re, in contrast to the isothermal case. Similarly, in non-isothermal flow, flow pattern is unchanged at different flow rate. This is also in contrast to the isothermal situation.

Wave Motion of a Compressible Viscous Fluid Contained in a Cylindrical Shell

1993 ◽  
Vol 115 (3) ◽  
pp. 302-312 ◽  
Author(s):  
J. H. Terhune ◽  
K. Karim-Panahi
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Imaginary Part ◽  
Fluid Velocity ◽  
Wave Number ◽  
Mode Shapes ◽  
Infinite Length ◽  
Complex Frequency ◽  
Compressible Viscous Fluid ◽  
Fluid Velocity Field

The free vibration of cylindrical shells filled with a compressible viscous fluid has been studied by numerous workers using the linearized Navier-Stokes equations, the fluid continuity equation, and Flu¨gge ’s equations of motion for thin shells. It happens that solutions can be obtained for which the interface conditions at the shell surface are satisfied. Formally, a characteristic equation for the system eigenvalues can be written down, and solutions are usually obtained numerically providing some insight into the physical mechanisms. In this paper, we modify the usual approach to this problem, use a more rigorous mathematical solution and limit the discussion to a single thin shell of infinite length and finite radius, totally filled with a viscous, compressible fluid. It is shown that separable solutions are obtained only in a particular gage, defined by the divergence of the fluid velocity vector potential, and the solutions are unique to that gage. The complex frequency dependence for the transverse component of the fluid velocity field is shown to be a result of surface interaction between the compressional and vortex motions in the fluid and that this motion is confined to the boundary layer near the surface. Numerical results are obtained for the first few wave modes of a large shell, which illustrate the general approach to the solution. The axial wave number is complex for wave propagation, the imaginary part being the spatial attenuation coefficient. The frequency is also complex, the imaginary part of which is the temporal damping coefficient. The wave phase velocity is related to the real part of the axial wave number and turns out to be independent of frequency, with numerical value lying between the sonic velocities in the fluid and the shell. The frequency dependencies of these parameters and fluid velocity field mode shapes are computed for a typical case and displayed in non-dimensional graphs.

scholarly journals Steady MHD Flow of Viscous Fluid between Two Parallel Porous Plates with Heat Transfer in an Inclined Magnetic Field

2015 ◽  
Vol 7 (3) ◽  
pp. 21-31 ◽  
Author(s):  
D. R. Kuiry ◽  
S. Bahadur
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Reverse Flow ◽  
Flow Behavior ◽  
Fluid Pressure ◽  
Mhd Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent Viscosity

The steady flow behavior of a viscous, incompressible and electrically conducting fluid between two parallel infinite insulated horizontal porous plates with heat transfer is investigated along with the effect of an external uniform transverse magnetic field, the action of inflow normal to the plates, the pressure gradient on the flow and temperature. The fluid viscosity is supposed to vary exponentially with the temperature. A numerical solution for the governing equations for both the momentum transfer and energy transfer has been developed using the finite difference method. The velocity and temperature distribution graphs have been presented under the influence of different values of magnetic inclination, fluid pressure gradient, inflow acting perpendicularly on the plates, temperature dependent viscosity and the Hartmann number. In our study viscosity is shown to affect the velocity graph. The flow parameters such as viscosity, pressure and injection of fluid normal to the plate can cause reverse flow. For highly viscous fluid, reverse flow is observed. The effect of magnetic force helps to restrain this reverse flow.

The Effects of Vibrations on Particle Motion in a Viscous Fluid Cell

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Samer Hassan ◽  
Masahiro Kawaji
Keyword(s):  
Viscous Fluid ◽  
Drag Force ◽  
Particle Motion ◽  
Fluid Model ◽  
Resonance Phenomenon ◽  
Fluid Viscosity ◽  
Mass Force ◽  
Amplitude Data ◽  
Viscous Fluid Model ◽  
Fluid Cell

The effects of small vibrations on particle motion in a viscous fluid cell have been investigated experimentally and theoretically. A steel particle was suspended by a thin wire at the center of a fluid cell, and the cell was vibrated horizontally using an electromagnetic actuator and an air bearing stage. The vibration-induced particle amplitude measurements were performed for different fluid viscosities (58.0cP and 945cP), and cell vibration amplitudes and frequencies. A viscous fluid model was also developed to predict the vibration-induced particle motion. This model shows the effect of fluid viscosity compared to the inviscid model, which was presented earlier by Hassan et al. (2004, “The Effects of Vibrations on Particle Motion in an Infinite Fluid Cell,” ASME J. Appl. Mech., 73(1), pp. 72–78) and validated using data obtained for water. The viscous model with modified drag coefficients is shown to predict well the particle amplitude data for the fluid viscosities of 58.5cP and 945cP. While there is a resonance frequency corresponding to the particle peak amplitude for oil (58.0cP), this phenomenon disappeared for glycerol (945cP). This disappearance of resonance phenomenon is explained by referring to the theory of mechanical vibrations of a mass-spring-damper system. For the sinusoidal particle motion in a viscous fluid, the effective drag force has been obtained, which includes the virtual mass force, drag force proportional to the velocity, and the Basset or history force terms.

Heat Transport by Countercurrent Blood Vessels in the Presence of an Arbitrary Temperature Gradient

1990 ◽  
Vol 112 (2) ◽  
pp. 207-211 ◽  
Author(s):  
J. W. Baish
Keyword(s):  
Thermal Conductivity ◽  
Temperature Gradient ◽  
Vascular Tissue ◽  
Asymptotic Methods ◽  
Three Dimensional ◽  
Conductive Materials ◽  
Arbitrary Temperature ◽  
The Mean ◽  
Conductive Fibers ◽  
Arteries And Veins

This paper presents a three-dimensional analysis of the temperature field around a pair of countercurrent arteries and veins embedded in an infinite tissue that has an arbitrary temperature gradient along the axes of the vessels. Asymptotic methods are used to show that such vessels are thermally similar to a highly conductive fiber in the same tissue. Expressions are developed for the effective radius and thermal conductivity of the fiber so that it conducts heat at the same rate that the artery and vein together convect heat and so that its local temperature equals the mean temperature of the vessels. This result allows vascular tissue to be viewed as a composite of conductive materials with highly conductive fibers replacing the convective effects of the vasculature. By characterizing the size and thermal conductivity of these fibers, well-established methods from the study of composites may be applied to determine when an effective conductive model is appropriate for the tissue and vasculature as a whole.

Nearly free-molecular slit flow at finite pressure and temperature ratios

1971 ◽  
Vol 50 (3) ◽  
pp. 565-577 ◽  
Author(s):  
P. Y. Wang ◽  
E. Y. Yu
Keyword(s):  
Mass Flow ◽  
Total Mass ◽  
Noble Gas ◽  
Order Correction ◽  
Linear Boltzmann Equation ◽  
Molecular Flow ◽  
First Order ◽  
Slit Flow ◽  
Isothermal Case ◽  
First Order Correction

An analytical study is made of nearly free-molecular flow of a noble gas from one reservoir to another through a two-dimensional slit, with finite pressure and temperature ratios across the slit. The fundamental solution of the linear Boltzmann equation is employed in the study. The total mass flow is calculated to the first-order correction terms, of the order of α ln α and α, where α is the inverse Knudsen number. The coefficients of these terms are in general multiple integrals, but they become explicit functions of the pressure and temperature ratios after the multiple integrations are carried out by using Krook collision model. When the general result is simplified to the isothermal case the first-order correction has a negative value, indicating the reduction of the total mass flow due to intermolecular collisions in the counter flows.

Sign in / Sign up

Export Citation Format

Share Document