The third edition in German should appear in the 1st semester of the year 2010. The 1st English edition owes its existence to the initiative and sponsor of the management of Sulzer Pumps.
Symbols, abbreviations, definitions
FOR specific erosion power PER = UR×ER Table 6.1 Disc friction power loss caused by balance device Table 3.6 Power loss Ps3 distributed in interphase sealing Tables. Specific work Ysch≡ Yth done by the impeller blades: Yth = g×Hth Table 3.3 Specific work Yth∞ done by the impeller blades with congruent flow on the blade.
Pump styles
MSD – Dual Volute Opposed Impeller Horizontally Split ISO 13709 (API 610) Type BB3 CP – Dual Volute Opposed Impeller Barrel Type.
1 Fluid dynamic principles
Flow in the absolute and relative reference frame
Conservation equations
- Conservation of mass
- Conservation of energy
- Conservation of momentum
According to [1.3] the measured pressure recovery reaches approximately 95% of the theoretical values calculated from Eq. Therefore, the change in angular momentum is equal to the sum of the external moments.
Boundary layers, boundary layer control
The thickness of the boundary layer then decreases; with accelerated flow correspondingly lower hydraulic losses are experienced. These equations show that the thickness of the boundary layer grows from the leading edge at x = 0 with the length of the flow path and the viscosity of the fluid.
Flow on curved streamlines
- Equilibrium of forces
- Forced and free vortices
- Flow in curved channels
The pressure in a curved duct decreases from the outside to the inside in the direction of the center of curvature according to Eq. To satisfy the continuity condition, fluid in the center of the channel is transported to the outside, so that the secondary flow outlined in Fig.
Pressure losses
- Friction losses (skin friction)
- Influence of roughness on friction losses
- Losses due to vortex dissipation (form drag)
They are shown in Figure 1.13 as a function of Reynolds number and relative roughness, [1.5]. The equivalence factor depends on the structure of the roughness – i.e. the machining process – and the orientation of the finishing marks with respect to the flow direction; ceq can therefore vary within wide limits.
Diffusers
If a certain deceleration ratio is specified, it is possible to determine the diffuser length required for maximum pressure recovery from Figure. It is important to realize that the allowable diffusion angle of a diffuser is by no means a universal constant (an opinion that is still often expressed) but that this is largely dependent on the length of the diffuser.
Submerged jets
Consider a fluid entering a tank at the rate co from a pipe and let the dimensions of the tank be large in relation to the pipe diameter. At the exit of the pipe, a jet of liquid is created that mixes with the contents of the tank through turbulence.
Equalization of non-uniform velocity profiles
The pressure loss coefficients given in Table 1.4 for sharp edged or rounded thick orifice plates can be applied to screens, perforated plates and similar elements. Note that the resistance coefficients in Table 1.4 are referred to the throat area; such coefficients must be converted by Eq. 1.3.5) to obtain values referred to the mean approach velocity.
Flow distribution in parallel channels, piping networks
The methods listed in Table 1.5 are not only used for the calculation of pipeline systems, but have a more general meaning. A combination of series-connected flow resistances according to Table 1.5 is always shown when a pressure difference is given and a flow rate is desired. An example is the calculation of the leakage flow rate through a stepped ring seal according to Table 3.7(1) using Eq. Table 1.5 can also be used to estimate how the rotor flow is distributed to the individual channels of the double spiral according to their different flow resistances, ch.
All pipe sections or components receive the same flow rate Q. ζ ¦ ARS = selected reference section 1.5.1 Pressure drop of individual.
2 Pump types and performance data
Basic principles and components
2.1, an inducer can be added to the fan inlet to improve suction performance (Chapter 7.7). The impeller can be described by the hub, the rear casing, the blades that transfer energy to the fluid and the front casing. Depending on the direction of the flow at the fan exit, we distinguish radial, semi-axial and axial fans.
In this type of pump, the diffusers include return vanes that direct the fluid to the next stage impeller.
Performance data
- Specific work, head
- Net positive suction head, NPSH
- Power and efficiency
- Pump characteristics
Main and specific work are independent of the density or type of medium. We distinguish between the (usually measured) NPSH of the pump that is required to completely or partially suppress cavitation (“NPSH required” or NPSHR) and the NPSH available in the installation (NPSHA). From Bernoulli's equation we can find the absolute pressure at the highest point of the impeller, located at a distance “a” above the rotor axis.
The required power P at the coupling is greater than the useful power, because it includes all the losses of the pump.
Pump types and their applications
- Overview
- Classification of pumps and applications
- Pump types
- Special pump types
Small inline pumps are often built as monobloc pumps, where the impeller is mounted at the end of the motor shaft. A center bushing in the middle of the rotor controls the leakage from the second to the first group of stages. An external pipe leads the oil from the heat exchanger to the top of the motor.
The fluid adhering directly to the discs moves at the circumferential speed of the rotor (in an absolute reference frame).
3 Pump hydraulics and physical concepts
One-dimensional calculation with velocity triangles
As a result of the blade blocking, c1m grows to c1m' so that the approach angle increases from β1 to β1'. If the approach angle falls below the blade angle (i1 > 0), the stagnation point is on the pressure surface of the blade. 1 With profiled slats, the effect of the blockage cannot be easily defined under certain circumstances.
Blade blockage is still present immediately before the rotor exit and the velocity is correspondingly greater than behind the trailing edge: c2m' = c2m×τ2, en.
Energy transfer in the impeller, specific work and head head
From numerical calculations it can be deduced that Mτ is typically 1% of the moment transmitted by the impeller when no recirculation is present1. Psch = schω=ρ La 2m 2h− 1m 1h (3.3) The specific work done by the blades is obtained by dividing Psch by the mass flow rate m flowing through the impeller (m = QLa ȡ), Chapter. There, the kinetic energy is largely converted into static pressure. 1.15) the first two terms represent the increase in static pressure in the impeller plus the impeller losses, Eq.
The energy Ysch transmitted to the fluid by the impeller causes a total pressure increase Ytot,La at the outlet of the impeller.
Flow deflection caused by the blades. Slip factor
Both expressions implicitly assume the idea of a wing congruent flow and consider the deviation of the real flow from the wing trailing angle. one). Before the neck, in the impeller channel itself, the flow is controlled more efficiently and deviates less from the angle (see profiles k and s in Fig. 3.3a). The circumferential component of the absolute velocity c2u at the impeller outlet is obtained from Eq.
This fact is not sufficiently reflected in the slip factor formula, which predicts an influence of the inlet diameter only above a certain limit value.
Dimensionless coefficients, similarity laws and specific speed specific speed
If the impeller is designed with different outside diameters or trailing edge shapes (1 to 6 in Fig. 3.8), the head decreases roughly with the square of the diameter according to Eq. Because nx and Qx are constant, the relationship between Q, H and n changes; this means that the specific speed increases. The specific speed should invariably be calculated using the performance data at the best efficiency point and the head per stage.
With two-entry impellers, the specific speed is defined in Europe by the flow rate per impeller side, Eq.
Power balance and efficiencies
Hydraulic losses due to friction and turbulent dissipation in all components between the suction and discharge nozzles are covered by the hydraulic efficiency ηh (Chap. 3.7). In the case of balancing flow this only applies if the QE returns to the suction nozzle. All these losses are called "internal losses" because they heat the fluid in the car.
In addition, the following efficiencies are used: the mechanical efficiency according to Eq. T3.5.6); the internal efficiency according to Eq. T3.5.5) and the volumetric efficiency according to Eq.
Calculation of secondary losses
- Disk friction losses
This equation includes the effects of the impeller sidewall opening geometry, as well as the roughness of the casing and impeller shrouds. When comparing with other sources, the different definitions of the torque coefficients must be taken into account (often the coefficients are defined to include the torque or friction power for both sides of the disk). Roughness of the rotating disk: The roughness of the stationary or rotating surface increases the friction power, provided that the roughness peaks protrude from the boundary layer thickness.
Casing wall roughness: If the rotor and casing have the same roughness, the fluid rotation in the rotor sidewall gap is independent of the roughness, en.
- Leakage losses through annular seals
- Power loss caused by the inter-stage seal
- Leakage loss of radial or diagonal seals
- Leakage losses in open impellers
- Mechanical losses
- Basic hydraulic calculations of collectors
- Hydraulic losses
- Statistical data of pressure coefficients, efficiencies and losses and losses
- Influence of roughness and Reynolds number
- Overview
- Efficiency scaling
- Calculation of the efficiency from loss analysis
- Minimization of losses
- Compendium of equations for hydraulic calculations
The rotation factor k can be estimated in different ways: (1) according to Eq. T3.7.2) as a function of Reynolds number and seal geometry; (2) reading from Fig. The effect of flow on head, efficiency and NPSHR can be approximated by Eqs. Determination of the efficiency of the prototype (subscript “a”) ηa = f(Rea, εa/da) based on the efficiency ηM = f(ReM, εM/dM) measured in the model test (subscript “M”).
Influence of the roughness of different components (impeller, diffuser, impeller sidewalls and housing) on the efficiency. The proportion of the friction losses in the hydraulic losses can be estimated for a given pump according to Table 3.8 and Chap. It depends on the specific speed, the type of pump and the geometry of the hydraulic components.
4 Performance characteristics
Head-capacity characteristic and power consumption
- Theoretical head curve (without losses)
- Real characteristics with losses
- Component characteristics
As a first approximation, however, it can be assumed that the slip factor γ is independent of the flow rate in the region without partial load recirculation. They increase with the square of the flow according to Zr = (1-ηh,opt) Hth,opt q*2. Therefore, it is assumed that the velocities in the pump increase in proportion to the flow rate.
The measurements evaluated in Fig. 3) The average relative velocity in the impeller wav = ½(w1 + w2) changes little with the flow velocity.
The diffuser losses are obtained by applying Bernoulli’s Equation (1.7) be- tween impeller and diffuser outlet
- Influence of pump size and speed
- Best efficiency point
- Prediction of pump characteristics
- The data at the best efficiency point are known from the design calculation
This is to increase the static pressure in the impeller and the diffuser triangle until the flow stops. Due to the short distance between the rotor exit and the diffuser throat, the flow hardly develops according to the conserved angular momentum. As a result, the ratio of secondary losses to energy consumption decreases with increasing Pu.
At q* > 1, the efficiency drops steeply, as the acceleration of the fluid from the impeller outlet to the throat region causes large losses in the diffuser.