Specific Energy Shells: Rotodynamic Pump Energy Efficiency Graph

When lines of constant specific energy for a variable-speed rotodynamic pump are presented on a differential head verse flow-rate graph, the result is a set of eccentric, inverted, parabola-like curves. In this paper, these lines are referred to as specific energy shells. It will be shown that energy consumption per unit volume pumped is not necessarily proportional to efficiency or speed for any given pumping system. However, specific energy shells give immediate insight into relative energy efficiencies across the entire range of flow rates. To demonstrate, a desktop case study will be presented where the reduction from speed control alone will be quantified, and the methodology will be repeated with a moderate passive system improvement. The result is a reduction in specific energy as pump speed is reduced despite a decline in efficiency. Secondary to this, as the pump speed is reduced further, the efficiency continues to decline while the specific energy increases, demonstrating that using speed reduction as a tool to reduce energy consumption has limitations that are pump- and system specific. Finally, it will be shown that specific energy has the same affinity relationship with speed as differential head \( \left(\frac{{\boldsymbol{E}}_{{\boldsymbol{S}}_{\mathbf{1}}}}{{\boldsymbol{E}}_{{\boldsymbol{S}}_{\mathbf{2}}}}\right)={\left(\frac{{\boldsymbol{n}}_{\mathbf{1}}}{{\boldsymbol{n}}_{\mathbf{2}}}\right)}^{\mathbf{2}}=\left(\frac{{\boldsymbol{H}}_{\mathbf{1}}}{{\boldsymbol{H}}_{\mathbf{2}}}\right) \) . The purpose of the case study and affinity relationship presentation is to demonstrate that the variable speed pump performance graph with specific energy shells overlaid can be used to estimate all of the pump-specific findings shown without further calculations required. This capacity is not available using the information traditionally presented on a variable speed pump performance graph. Therefore, specific energy shells should be included as an option on variable speed pump performance graphs, and pump package providers should work toward including all component efficiencies in a single graph.