I often witness end users operating pumps to the left side of the curve, away from the best efficiency point (BEP) and near shutoff. This is not the ideal area because of issues with shaft deflection, cavitation and recirculation, all of which lead to a reduction in pump reliability. There are several other reasons to avoid operating in this region as well.
Minimum flow is the operating area where centrifugal pumps will quickly get into trouble. The power introduced into a pump by the driver will manifest as energy or work—either as a useful flow with a corresponding head or as heat, vibration, noise (acoustic energy) or a combination of all these. Because no pump is 100 percent efficient, the energy not used in the work for the head and flow will show up as one of these other items.
Technically, four factors affect minimum flow: fluid temperature rise, minimum stable flow, internal recirculation and thrust capacity.
For most cases, we can simplify these factors and just look at two main areas. The first area is under the category of mechanical issues, and the other is thermal issues. A minimum continuous flow rate for a pump should be determined for mechanical and thermal factors. The higher of the two becomes the minimum flow rate for that pump.
When the pump is operated away from BEP, the radial thrust will increase dramatically. For a single volute pump, it is close to a hyperbolic function. The shaft will deflect and create issues with the bearings and seals, dramatically shortening their useful life. Also, the flow velocity (angle/profile) will not match the impeller vane speeds (velocity/inlet angle/angle of incidence), and suction recirculation will occur, creating fluid stalls and cavitation.
The shaft deflection ratio (L3/D4) comes into play in these calculations: A low L3/D4 ratio will mitigate the deleterious effects.
Minimum continuous stable flow (MCSF) is defined as the flow rate below which the pump should not be operated. The American Petroleum Institute (API) will define it as operating without exceeding specified vibration limits. The actual calculation of this MCSF rate is a function of numerous factors that include suction energy (in my opinion, suction energy is otherwise an outdated concept), suction-specific speed and specific speed (impeller geometries). Pay particular attention to factors that affect the onset of suction recirculation and exit turbulence at the vane tips as these result in vortex cavitation.
Some specifications tend to simplify these calculations and state that minimum flow should be a percentage of the BEP flow rate. For example, API 610 states that MCSF will be no less than 60 percent allowable value (70 percent is preferred). ANSI B73.1 states in paragraph 5.1.6 that "pumps shall be designed to operate continuously between 110 percent of BEP and the minimum flows shown in Table 5." There is more to this specification, which I will not cover here, but please note that Table 5 values do not take thermal flow factors into consideration.
While the energy put into a pump running at minimum flow (for other than head and flow) may yield vibration and noise, it is most likely to manifest as heat. Another possibility is heating the fluid to the point of vaporizing the fluid and cavitating or even exceeding the design limits of the casing (due to the vaporization of the fluid to a gas and causing casing rupture). The rate at which the temperature will rise in a pump with a closed discharge valve can be calculated using Equation 1.
For my metric (SI) friends, the temperature TR is degrees C per second. The power will be in kilowatts (kW), the specific heat for water is 4.19 joules per gram-degree C, and the pump casing volume will be in liters. SI calculations can also drop the 0.085 in the numerator.
Some of the heat from the temperature rise will be dissipated to ambient. When the pump's ability to dissipate the heat is exceeded by heat generation, the pump and fluid temperature rise quickly. Insulation and ambient temperature affect heat balance.
When calculating the brake horespower (BHP) at this "no flow" condition, realize that no flow is produced downstream of the pump, but it is produced internally. Most manufacturers use the casing volume as a minimum plus a flow rate factor that is a function of the pump size and number of stages. The pump efficiency at these low flows is low and hard to pinpoint.
The time required for the fluid to vaporize can be calculated by dividing the temperature rate (see Equations 2 and 3) into the value of the differential temperature (∆T).
The ∆T is the temperature difference between the pump suction temperature and the fluid saturation temperature.
The temperature increase in the pump, especially at low flow, is dependent on the liquid's rate of flow through the pump.
Minimum continuous thermal flow (MCTF) is usually not the most limiting factor in determining a pump's minimum flow. Typically the mechanical aspects will be the limiting factor, but do not ignore the thermal flow considerations.