The classic angular momentum flow meter has four major components: a main shaft that may be rotated by a turbine or a motor; a stationary flow straightener; an impeller (momentum wheel); and a speed wheel drum. During operation, the fluid flows through the turbine which causes the turbine to rotate. The turbine is connected to the shaft and therefore the shaft rotates in unison with the turbine.
Next, the fluid passes through a stationary flow straightener. The stationary flow straightener is not coupled to the shaft or the turbine. The purpose of the flow straightener is to remove as much of the angular momentum from the fluid as possible because unaccounted for angular momentum will cause an error in the measurement. For example, turbulence or swirl may be introduced into the fluid by any number of elements including bends in the pipe in which the fluid travels or the turbine. The flow straighteners help remove turbulence and swirl. Ideally, as the fluid exits the stationary flow straightener, all angular momentum with respect to the rotational axis of the flow meter has been removed.
Finally, the fluid passes through the impeller and drum. Typically, the impeller is located inside the drum to form a measurement assembly. The drum forms an outer enclosure of the measurement assembly and the impeller is located on the interior of the drum. Both the impeller and the drum are in rotation about the axis. However, the drum and the impeller are connected to the flow meter in different ways. The drum is rigidly affixed to the shaft such that the drum is forced to rotate in unison with the turbine and the shaft. The impeller, is attached to a rotating member of the flow meter, for example the shaft or the drum, by a spring element, such as a torsional spring.
The fluid, which ideally exits the flow straightener with no angular momentum with respect to the shaft, enters the impeller and the drum. The impeller and the drum are rotating with the same speed as the shaft. Consequently, the fluid is accelerated to match the rotation of the impeller and the drum. However, because the impeller is attached to the shaft or other rotating member of the flow meter via a spring, the impeller is caused to lag behind the drum. The forced rotation of the impeller changes the rotational velocity of the fluid as it passes through and increases the fluid's angular momentum. The increase in angular momentum of the fluid can be measured by calibrating the spring connecting the impeller to the shaft to obtain the torque required to force the impeller to rotate as the fluid passes through. The equation for torque is:T={dot over (m)}*ω*r2 Where: T=torque; {dot over (m)}=mass flow rate; ω=angular velocity; and r=radius of gyration of the mass flow.
One method of measuring the torque via the spring is to measure the lag of the impeller with respect to the drum as they both rotate around the axis of the shaft. Although both the drum and the impeller will tend to rotate at the same velocity, the torque imparted by the fluid on the impeller will cause the spring to deflect resulting in the impeller lagging the drum as they both rotate around with the shaft. The lag may be measured and from which the torque required to be imparted on the impeller to increase the fluid's angular momentum may be calculated.
A common method of measuring the lag between the impeller and the drum is to place a magnet on the outside of both the impeller and the drum. Stationary wire coils may then be positioned so that they come in close proximity to the magnets as the impeller and drum rotate. The rotating magnets will induce a small electric pulse in the electric coils each time they pass. The electric pulse can be detected by electronic circuitry and the lag in phase determined based on when the magnet associated with the drum and when the magnet associated with the impeller pass by their respective coils. The lag can be used to calculate the torque based on the spring constant. For any given spring constant, the smaller the phase shift the less torque required to rotate the impeller through the fluid. In contrast, the larger the phase shift the more torque that is required to rotate the impeller through the fluid. The torque required to change the angular momentum of the fluid can then be translated into the mass flow rate of the fluid. The time Δt between two pulses due to a phase lag or lag angle ζ is
      Δ    ⁢                  ⁢    t    =      ζ    ω  where
  ζ  =            T      c        =                            m          .                *        ω        *                  r          2                    c      and c is the spring constant. Substituting for ζ gives
      Δ    ⁢                  ⁢    t    =                    r        2            c        *          m      .      or Δt=k*{dot over (m)} which shows Δt becomes directly proportional to {dot over (m)}.
The above described design uses the principles of conservation of momentum to measure the mass flow rate of the fluid traveling through the flow meter. Ideally, the fluid leaves the flow straightener with no rotation about the central axis of the flow meter. As the fluid passes through the impeller and drum (or measurement assembly), the fluid is accelerated to rotate about the central axis of the flow meter. Because of the physics of conservation, the amount of energy that is required to increase the rotation of the fluid around the axis of the flow meter may be translated into the mass flow of the fluid passing through the flow meter.
Although the above described flow meter design can measure the mass flow rate of a fluid passing through, a number of errors that affect the accuracy of the device are inherent in its design. For example, as the fluid passes from the flow straightener into the impeller and drum assembly, the fluid passes through a shearing plane created by the difference in angular velocity of the rotating impeller and the stationary flow straightener. The shearing force created at the shearing plane is a frictional force that increases the amount of energy needed to rotate the liquid with the impeller. If the shearing force is constant, it may be factored out of the calculations and the mass-flow rate may be determined relatively accurately. However, the shearing force is dependent on the viscosity of the liquid which may change with temperature or from one fluid to another. Even similar types of fluid from different locations or suppliers, like for example Kerosene for jet engines, may have different viscosities. Therefore, the shearing force may vary with both the kind of fluid passing through the flow meter and the temperature of the fluid flowing through the flow meter. The varying shear force creates an error in the mass flow calculation that is difficult to account for. A large variable shearing force can prevent the mass flow meter from making accurate measurements.
Furthermore, it may be difficult to remove or reduce the shearing force with current designs. In order to obtain a large measuring torque to maximize the accuracy of the flow meter, the angular momentum added to the fluid should be maximized. In order to maximize the angular momentum added to the fluid as it pass through the flow meter, the distance between the fluid flow path and the rotational axis of the flow meter should be maximized. Maximizing the distance from the rotational axis to the flow path also increases the error causing torque caused by the shearing forces because the length of the torque arm is increased. This complicates the process of trying to minimize the measurement error in current mass flow meter designs.