On the Stability for a Certain Degenerate Type of Disturbance of Viscous Fluid Flow Between Parallel Walls

Author(s):  
S. I. Pai
Author(s):  
S. Goldstein

If we consider, by the method of small oscillations, the stability of a viscous fluid flow in which the undisturbed velocity is parallel to the axis ofxand its magnitudeUis a function ofyonly (x, y, zbeing rectangular Cartesian co-ordinates), and if we assume that any possible disturbance may be analysed into a number (usually infinite) of principal disturbances, each of which involves the time only through a single exponential factor, then it has been proved by Squire, by supposing the disturbance analysed also into constituents which are simple harmonic functions ofxandz, and considering only a single constituent, that if instability occurs at all, it will occur for the lowest Reynolds number for a disturbance which is two-dimensional, in thex, yplane. Hence only two-dimensional disturbances need be considered. The velocity components in the disturbed motion will be denoted by (U+u, v). Since only infinitesimal disturbances are considered, all terms in the equations of motion which are quadratic inuandvare neglected. Whenuandvare taken to be functions ofymultiplied byei(αx−βi), the equation of continuity becomesand the result of eliminating the pressure in the equations of motion then gives the following equation forv, where ν is the kinematic viscosity of the fluid:


Author(s):  
Yi Shi ◽  
Jianjun Zhu ◽  
Haoyu Wang ◽  
Haiwen Zhu ◽  
Jiecheng Zhang ◽  
...  

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%.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
M. Zubair Akbar Qureshi ◽  
S. Bilal ◽  
M. Y. Malik ◽  
Qadeer Raza ◽  
El-Sayed M. Sherif ◽  
...  

AbstractMatrix nanocomposites are high performance materials possessing unusual features along with unique design possibilities. Due to extraordinary thermophysical characteristic contained by these matrix nanocomposites materials they are useful in several areas ranging from packaging to biomedical applications. Being an environment friendly, utilization of nanocomposites offer new technological opportunities for several sectors of aerospace, automotive, electronics and biotechnology. In this regards, current pagination is devoted to analyze thermal features of viscous fluid flow between orthogonally rotating disks with inclusion of metallic matrix nanocomposite (MMNC) and ceramic matrix nanocomposites (CMNC) materials. Morphological aspects of these nanomaterials on flow and heat transfer characteristics has been investigated on hybrid viscous fluid flow. Mathematical structuring of problem along with empirical relations for nanocomposites materials are formulated in the form of partial differential equations and later on converted into ordinary differential expressions by using suitable variables. Solution of constructed coupled differential system is found by collaboration of Runge–Kutta and shooting methods. Variation in skin friction coefficient at lower and upper walls of disks along with measurement about heat transfer rate are calculated against governing physical parameters. Impact of flow concerning variables on axial, radial components of velocity and temperature distribution are also evaluated. Contour plots are also drawn to explore heat and thermal profiles. Comparison and critical analysis of MMNc and CMNc have been presented at lower and upper porous disks. Our computed analysis indicates that hybrid nanofluids show significant influence as compared to simple nanofluids with the permutation of the different shape factors.


2017 ◽  
Vol 26 (1) ◽  
pp. 69-78 ◽  
Author(s):  
M. Awais ◽  
U. Bukhari ◽  
A. Ali ◽  
H. Yasmin

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