# Review: A Survey on Configurations and Performance of Flow-Mode MR Valves
## 4 Analysis
### Benchmark Valve(s)  
Let us consider briefly the benchmark in Figure 6(a). As already mentioned, it involves a transversely wounded coil onto a core. The core and the outer ring form the annulus for the fluid to pass through. At the same time, they constitute elements of the magnetic circuit of the valve. The current in the coil produces the magnetic flux in the structure. While passing through the annular gap, the flux energizes the fluid, thus developing a yield stress in the material. As a result, the fluid's resistance-to-flow is built up, and the output force ( pressure drop) increases according to the induced flux level. Effectively, the changes in the rheology of the material translate into the relationship between the pressure drop \(\Delta P\) and the flow rate \(Q\) illustrated in Figure 8(a).  
The benchmark configuration is structurally simple and compact, and it delivers satisfactory \(\Delta P-Q\) envelopes as demonstrated in the analysis at the end of the section. It has been the basis for many of the other configurations developed over the last 30 years. Despite giving the engineer a sufficient amount of freedom in tuning the output of the valve according to the requirements, its application may result in numerous compromises. First of all, from the EM's perspective, saturating the core in the area below the coil can hardly be avoided. Second, the usual modifications of the core cross-section area below the coil window are often difficult due to packaging constraints. Last, the configuration provides little flexibility in the coil assembly placement. For instance, our analysis of the benchmark valve implementations in the available references has led us to conclude that most engineering efforts to avoid saturation in this region resulted in hardly efficient configurations with shallow and wide coil windows and short magnetic poles or substituting the core material.  
In many analyzed configurations the active area ratio was below \(1/2\).  
It is evident that the configuration in Figure 6(a) shares many similarities with the valves revealed in Figure 6(b), as well as Figure 6(c). The former has a unique feature of intrinsic asymmetric \(\Delta P-Q\) envelopes in either direction of motion (achieved due to different flow losses) whereas the latter shows the annulus shifted below the coil window. Despite certain advantages [77], it can be argued that the valve in Figure 6(c) may be more liable to saturation. Moreover, the gap's smaller circumferential width (compared to the benchmark valve) may translate into steeper slopes of the \(\Delta P-Q\) characteristics. This can be coped with by increasing the gap height (decreasing the yield stress in the annulus as a result, and thus degrading the pros of the particular valve's structure).  
As a way of approximation, the magnetic field in the flow channel is radially uniform in the benchmark structure. However, it can be disrupted on purpose. [PERSON] and [PERSON] [43] analyzed the simple structure with an eccentric gap. In this concept, the gap height varies continuously in the radial direction, and thus, the resulting yield stress. As a result, various breakaway pressures are achieved at each point of the gap.