## Design And Operation Of Models

Model Scale Scale effects are less as model size increases but construction and operation costs increase with model size, so a compromise must be made. In general, the formation of vortices, both free surface and submerged, is highly responsive to approach flow patterns, and it is important to select a geometric scale that achieves Reynolds numbers large enough to keep the flow turbulent and to meet the fluid mechanic criteria for minimizing scale effects.13 Also, one should consider other factors such as access for instruments, accurate flow measurements, and ease of modification in selecting a proper scale.

Information on preferred minimum values of Reynolds number and Weber number, discussed earlier, may be used in designing a model and deciding geometric scale. However, adhering to these limits does not, in itself, guarantee negligible scale effects in a Froude model because these limits are based on tests run under ideal laboratory conditions. In real situations, there is usually more than one source of vorticity generation of unknown extent, and a generalization of scale effects for all cases would be inappropriate. To compensate for such unknown scale effects, a common practice is to test a model at higher-than-Froude scaled flows.

A special test procedure involving high temperatures may be used to determine any scale effects and to project the model results to prototype ranges of Reynolds numbers.2 The water temperature in the model is varied over a range, say 50 to 120°F (10 to 49°C), and flow velocities in the pipes are varied over a range of values, if possible, up to the prototype velocities. Vortexing and other flow patterns over a range of Reynolds numbers are obtained from these tests and can be used to evaluate any possible scale effects. A prediction of the prototype performance can be made based on these tests.

Extent of Model It is very important to include a sufficient length of approach channel in the model because approach flow nonuniformities contribute greatly to vortex formation and swirl. The decision on what approach length should be included is usually based on the experience and engineering judgment of the model designer. The requirement is essentially the proper simulation of approach velocity profile to the intake and then on to the pump bays. In some cases, considering the cost and time involved in including a sufficient channel length in a pump intake model, a separate, smaller model can be built to determine the approach flow patterns to the intake and these flow patterns then simulated in the pump intake model.18

Figure 4a shows a 1:10 geometric scale model of a four-bay pump intake, with each pump designed to draw 140,000 gpm (312 cfs or 8.83 m3/s) flow. Figure 4b shows a 1:18 geometric scale model pump intake for a flood control project involving several low head high flow pumps—each handling 360,000 to 450,000 gpm (800 to 1,000 cfs) at 12 ft head (22.68 to 28.35 m3/s at 3.65 m head).

Modeling of Screens and Gratings In addition to providing protection from debris, screens suppress nonuniformities of approach flow. The aspects of flow through screens that are of concern in a model study are (1) energy loss in the fluid passing through the screen, (2) modification of the velocity profile, and (3) production of turbulence. As all these factors could affect vortex formation in a sump with approach flow directed through screens, a proper modeling of screen parameters is important.

The fluid passing through the screen loses energy at a rate proportional to the drop in pressure, and this loss dictates the effectiveness of the screen in altering velocity profiles. The pressure drop across the screen is analogous to the drag induced by a row of cylinders in a flow field and can be expressed in terms of a pressure drop coefficient K (or, alternately, a drag coefficient), defined as19

where Ap = drop in pressure across screen ua = mean velocity of approach flow to screen AH = head loss across screen

The loss coefficient is a function of three variables: (1) screen pattern, (2) screen Reynolds number Rs = uadw/v, where dw is the wire diameter of the screen, and (3) solidity ratio S', the ratio of closed area to total area of screen (Section 8.1).

If S' and the wire mesh pattern are the same in the model and prototype screens, the corresponding values of K are a function of Rs only. This is analogous to the drag coefficient in a circular cylinder. At values of Rs greater than about 1,000, K becomes practically independent of Rs.19 However, for models with low approach flow velocity and fine wire screens, it is necessary to ascertain the influence of Rs on K for both model and prototype screens before selecting screens for the model that are to scale changes in velocity distribution.

Velocity modification equations relating the upstream and downstream velocity profiles usually indicate a linear relationship between the two, the shape and solidity ratio of the screen, and the value of K.20 If wire shapes and solidity ratios are the same in model and prototype, it is possible to select a suitable wire diameter to keep the values of K approximately the same for the model and prototype screens in the corresponding Reynolds number ranges. This produces a head loss across the model screen that is scaled to the geometric scale of the model and that produces identical velocity modifications in model and prototype. Some model designers consider it a conservative approach to leave out the screens in the model altogether, under the assumption that this omission will only worsen the nonuniformity of the approach flow. This approach is not recommended unless it is not practically possible to select an appropriate model screen.

Modeling of Pumps The exterior submerged surfaces of the pump bowl assembly and, for wet-pit pumps, the column including the bell mouth must be modeled to scale as well as the interior geometry from the bell mouth perimeter to the impeller eye. This is to ensure that flow patterns approaching the impeller are properly simulated.

Prerotation induced by the pump's rotating element is discussed in Sections 2.3 and 10.1 and in References 21 to 24. It has been shown that the rotating element does not affect upstream flow patterns when the pump is operated at design flow, and hence,

including the rotating element in a pump intake study is not necessary. When the pump is operated at less than rated flow, a degree of swirl is induced upstream of the rotating element. This swirl increases rapidly at flow rates less than 45% of rated flow as reversed flow out of the impeller intensifies, and this may affect vortex activity in the pump well and flow distribution to the pump.

Model Operation Operating a model at the prototype suction pipe velocity is thought to be a conservative method to compensate for excessive viscous energy dissipation and the consequent less intense model vortices in a Froude model.17 This method is often referred to as the Equal Velocity Rule. Operating a model at a higher than Froude scaled velocity should be considered a reasonable procedure for evaluating scale effects. However, operating a model based on the equal velocity rule may not be advisable unless the model is large enough, say at least a 1:4 scale model, because increasing the flow to many times the Froude scaled flow while keeping a scaled submergence could distort the approach flow patterns and turbulent intensities and, thus, cause unrealistic results. In general, a velocity increase to about 1.5 times the Froude scaled velocity can be considered reasonable. More appropriately, the information contained in References 25 and 26 may be used to decide the velocity ratio for exaggeration, which often is considered a function of model scale. If the final recommended design does not show any coherent core vortices in a model, no large scale effects should be expected, and operating the model at higher than Froude scaled flows may be unnecessary in such cases.27

Model Cost The cost of model studies varies considerably and is dependent on such factors as number of pump bays, number of operating conditions, and complexity of approach flow. Typically, $40,000 to $90,000 (in 1999 U.S. dollars) can be expected to cover the range from simple one- or two-bay sumps to multibay installations with complex approach flow and several operating modes.

## Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

## Post a comment