Unsteady flows induced by a point source or sink in a fluid of finite depth

2016 ◽  
Vol 28 (3) ◽  
pp. 357-379 ◽  
Author(s):  
T. E. STOKES ◽  
G. C. HOCKING ◽  
L. K. FORBES

The time-varying flow in which fluid is withdrawn from or added to a reservoir of infinite or arbitrary finite depth through a point sink or source of variable strength beneath a free surface is considered. Backed up by some analytic work, a numerical method is used, and the results are compared with previous work on steady and unsteady flows. In the case of withdrawal for an impulsively started flow, it is found that the critical flow rate increases with reservoir depth, although it changes little as the depth increases beyond double the sink submergence depth. The largest flow rate at which steady solutions can evolve in source flows follows a similar pattern although at a considerably higher value. Simulations indicate that some of the previously calculated steady state solutions at higher flow rates may be unstable, if they exist at all.

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
A. Narain ◽  
N. Ajotikar ◽  
M. T. Kivisalu ◽  
A. F. Rice ◽  
M. Zhao ◽  
...  

Use of a conventional orifice-plate meter is typically restricted to measurements of steady flow rates. For any gas flowing within a duct in a pulsatile manner (i.e., large amplitude mass flow rate fluctuations relative to its steady-in-the-mean value), this paper proposes a new and effective approach for obtaining its time-varying mass flow rate at a specified cross section of an orifice meter. The approach requires time-varying (dynamic) pressure difference measurements across an orifice-plate meter, time-averaged mass flow rate measurements from a separate device (e.g., Coriolis meter), and a dynamic absolute pressure measurement. Steady-in-the-mean turbulent gas flows (Reynolds number ≫2300) with low mean Mach numbers (<0.2) exhibit effectively constant densities over long time-durations and are often made pulsatile by the presence of rotary or oscillatory devices that drive the flow (compressors, pumps, pulsators, etc.). In these pulsatile flows, both flow rate and pressure-difference fluctuation amplitudes at or near the device driver frequency (or its harmonics) are large relative to their steady mean values. The time-varying flow rate values are often affected by transient compressibility effects associated with acoustic waves. If fast Fourier transforms of the absolute pressure and pressure-difference measurements indicate that the predominant frequency is characterized by fp, then the acoustic effects lead to a nonnegligible rate of change of stored mass (associated with density changes) over short time durations (∼ 1/fP) and modest volumes of interest. As a result, for the same steady mean mass flow rate, the time variations (that resolve these density changes over short durations) of mass flow rates associated with pulsatile (and turbulent) gas flows are often different at different cross sections of the orifice meter (or duct). Together with the experimental measurements concurrently obtained from the three recommended devices, a suitable computational approach (as proposed and presented here) is a requirement for effectively converting the experimental information on time-varying pressure and pressure-difference values into the desired dynamic mass flow rate values. The mean mass flow rate measurement assists in eliminating variations in its predictions that arise from the use of turbulent flow simulation capabilities. Two independent verification approaches establish that the proposed measurement approach works well.


Author(s):  
E. M. A. Vermunt ◽  
K. A. J. Bruurs ◽  
M. S. van der Schoot ◽  
B. P. M. van Esch

Abstract A new diffuser design is developed for a low specific speed, multistage pump. In this design the diffuser and the de-swirl vanes are integrated into single vanes. This creates diffuser channels that extend from behind the impeller exit through the cross-over, up to the eye of the next stage impeller. Experiments show the occurrence of a saddle type instability in the head curve. At a critical flow rate of close to 50% of the flow rate at Best Efficiency Point (BEP), the head drops by 7% of the head at BEP. In this study Computational Fluid Dynamics (CFD) are used in an effort to understand the underlying flow phenomena. The head curve that is obtained with the transient CFD simulations contains a saddle type instability at a flow rate that is approximately the same as in the experiments, but with a lower magnitude. At flow rates higher than the critical flow rate, the predicted head and power are in very good agreement with the experimental data. At flow rates lower than the critical flow rate, the head and power are slightly over-predicted. An analysis of the pressure distribution in the pump reveals that the head loss at different flow rates in the diffuser shows a discontinuity at the critical flow rate. Since both the impeller head and the head loss in the vaneless gap increase continuously for decreasing flow rate, this is an indication that the cause of the head instability lies in the diffuser. Moreover, a strong increase in the variability of head and power at flow rates below the critical flow suggests that the phenomenon is unsteady. Flow patterns in the impeller and in the diffuser, as calculated by CFD, show a high degree of periodicity and are very similar for flow rates down to the critical flow rate. However, for lower flow rates the flow pattern changes completely. A single rotating stall cell is observed that causes two or three neighboring diffuser channels to stall, leading to a significantly lower flow rate or even a reversed flow. This stall pattern rotates in the direction of impeller rotation at a very low frequency of approximately 3.3% of the impeller rotation frequency.


The flow of liquid helium II has been investigated under gradients of pressure and temperature in slits of 1 μ diameter. Besides the flow rate, the heat current and the pressure difference at the ends of the slit, the pressure at an intermediate point within the slit has been determined. It was found that for superflow the entire drop in pressure and temperature occurs at the narrowest place in the slit. In the remainder of the slit mass flow takes place under effectively zero gradient of pressure or temperature. The experiments also indicate the existence of a critical flow rate beyond which frictional dissipation makes its appearance. The critical rate was determined by four different criteria which yielded consistent results. The temperature dependence of the critical rate is similar to that observed in the helium II film. With flow under a temperature gradient and for higher flow rates the hydrostatic pressure within the slit was found to drop below that at the ends and an explanation for this effect has been suggested. Some experiments with wider slits have shown that in these even for small velocities the transport is a mixture of superflow and normal flow which renders the phenomena very complex.


2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Majid Bizhani ◽  
Ergun Kuru

An experimental program was conducted to investigate turbulent flow of water over the stationary sand bed deposited in horizontal annuli. A large-scale horizontal flow loop equipped with the state-of-the-art particle image velocimetry (PIV) system has been used for the experiments. Experiments were conducted to measure the instantaneous local velocity profiles during turbulent flow and examine the impact of the presence of a stationary sand bed deposits on the local velocity profiles, Reynolds shear stresses and turbulence intensities. Results have shown that the existence of a stationary sand bed causes the volumetric flow to be diverted away from the lower annular gap. Increasing the sand bed height causes further reduction of the volumetric flow rate in the lower annulus. Velocity profiles near the surface of the bed deposits showed a downward shift from the universal law in wall units indicating that the flow is hydraulically rough near the sand bed. The equivalent roughness height varied with flow rates. At flow rates less than the critical flow rate, the Reynolds stress profile near the bed interface had slightly higher peak values than that of the case with no sand bed. At the critical flow rate, however, the peak Reynolds stress values for the flow over the sand bed was lower than that of the case with no bed. This behavior is attributed to the bed load transport of sand particles at the critical flow rate.


1982 ◽  
Vol 104 (1) ◽  
pp. 211-214
Author(s):  
J. W. Murdock

This paper is concerned with the computation of the theoretical critical flow of dry saturated steam through passages over a range of 1 psia (7 kPa) to the critical pressure of 3208.2 psia (22.12 MPa). Two computational methods are used: a theoretical method using ideal gas relations, and a flow maximization method using actual saturated steam properties. An equation is developed and based on the theoretical equation that yields flow rates that have an average deviation of 0.1 percent and a maximum deviation of 0.3 percent from the flow rate found by flow maximization. It is also demonstrated that Napier’s equation currently recommended by PTC 25.3-1976 “Safety and Relief Valves” is unsatisfactory for the calculation of theoretical critical flow rates.


1988 ◽  
Vol 53 (4) ◽  
pp. 788-806
Author(s):  
Miloslav Hošťálek ◽  
Jiří Výborný ◽  
František Madron

Steady state hydraulic calculation has been described of an extensive pipeline network based on a new graph algorithm for setting up and decomposition of balance equations of the model. The parameters of the model are characteristics of individual sections of the network (pumps, pipes, and heat exchangers with armatures). In case of sections with controlled flow rate (variable characteristic), or sections with measured flow rate, the flow rates are direct inputs. The interactions of the network with the surroundings are accounted for by appropriate sources and sinks of individual nodes. The result of the calculation is the knowledge of all flow rates and pressure losses in the network. Automatic generation of the model equations utilizes an efficient (vector) fixing of the network topology and predominantly logical, not numerical operations based on the graph theory. The calculation proper utilizes a modification of the model by the method of linearization of characteristics, while the properties of the modified set of equations permit further decrease of the requirements on the computer. The described approach is suitable for the solution of practical problems even on lower category personal computers. The calculations are illustrated on an example of a simple network with uncontrolled and controlled flow rates of cooling water while one of the sections of the network is also a gravitational return flow of the cooling water.


Designs ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 4
Author(s):  
Dillon Alexander Wilson ◽  
Kul Pun ◽  
Poo Balan Ganesan ◽  
Faik Hamad

Microbubble generators are of considerable importance to a range of scientific fields from use in aquaculture and engineering to medical applications. This is due to the fact the amount of sea life in the water is proportional to the amount of oxygen in it. In this paper, experimental measurements and computational Fluid Dynamics (CFD) simulation are performed for three water flow rates and three with three different air flow rates. The experimental data presented in the paper are used to validate the CFD model. Then, the CFD model is used to study the effect of diverging angle and throat length/throat diameter ratio on the size of the microbubble produced by the Venturi-type microbubble generator. The experimental results showed that increasing water flow rate and reducing the air flow rate produces smaller microbubbles. The prediction from the CFD results indicated that throat length/throat diameter ratio and diffuser divergent angle have a small effect on bubble diameter distribution and average bubble diameter for the range of the throat water velocities used in this study.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Karine Arrhenius ◽  
Oliver Büker

AbstractThe study presents an optimised method to correct flow rates measured with a LFE flowmeter pre-set on methane while used for gas mixtures of unknown composition at the time of the measurement. The method requires the correction of the flow rate using a factor based on the viscosity of the gas mixtures once the composition is accurately known. The method has several different possible applications inclusive for the sampling of biogas and biomethane onto sorbent tubes for conformity assessment for the determination of siloxanes, terpenes and VOC in general. Five models for the calculation of the viscosity of the gas mixtures were compared and the models were used for ten binary mixtures and four multi-component mixtures. The results of the evaluation of the different models showed that the correction method using the viscosity of the mixtures calculated with the model of Reichenberg and Carr showed the smallest biases for binary mixtures. For multi-component mixtures, the best results were obtained when using the models of Lucas and Carr.


2021 ◽  
Vol 232 (4) ◽  
pp. 1413-1424
Author(s):  
Rami Ahmad El-Nabulsi

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