IMPLEMENTATION OF KARNEY–TIJSSELING–GUIDAOUI TRANSIENT ENERGY FRAMEWORKS IN THE NUMERICAL ANALYSIS AND DESIGN OF A BIFURCATED GRAVITY IMPULSE FLOW FORMER (GIF²): AN ENTHALPY‑BASED ENERGY ANALYSIS

Classical hydraulic engineering treats transient processes such as water hammer as parasitic phenomena that should be avoided [1–4]. In contrast, this work demonstrates that controlled hydraulic transients can be utilized for the temporary concentration and redistribution of energy within a hydraulic cycle [10]. We present a numerical energy analysis of the GIF² system—a novel hydraulic converter operating under a minimal gravitational head of 0.9 m. The system self-organizes into a bifurcated flow structure: the main supply branch generates discrete high-energy liquid modules (141.3 L, 120 atm), while the control branch dissipates small sacrificial modules (0.26 L, 3.3 kJ) that provide synchronization and hydraulic isolation. The analysis employs a local volumetric energy density ε(t) = (P − Patm) + ½ρv², evaluated at fixed spatial control points [1, 19]. This quantity represents the specific mechanical work of the flow (the enthalpy-related pressure contribution together with the kinetic component) per unit volume [22, 23]. The true elastic energy (fluid compression and pipe wall deformation) is evaluated separately and is small (< 0.8% of the integral work potential of the module). Key results: During formation, the module is kinematically isolated in volume but energetically open. Its state is characterized by the integral quantity Hmax = (P − Patm)V, which is interpreted not as stored energy but as the maximum pressure work that can be realized during the displacement process to atmospheric pressure. After losses (reflections 18.6%, stabilizer 15.3%, control branch 0.2%), the energy delivered at the nozzle is Hdel = 1125.5 kJ, corresponding to a conversion efficiency η = Hdel/Hmax = 66.1%. The high cyclic coefficient KEPcycle = Hdel / Egravity = 574 reflects not energy amplification, but its temporal concentration and redistribution within the cycle (accumulation over ~0.4 s and release over ~2 ms), as well as dynamic transformation described by the Joukowsky relation (2c/v ≈ 136). An additional contribution is provided by internal energy recovery from the previous cycle (controlled rarefaction to p ≈ −0.8 atm), which represents energy redistribution within the system and provides approximately 38.5 kJ per cycle for pre-acceleration of the flow. The system operates in an accumulative transient regime with a Karney φ-index of φ = 0.745 [11], and the observed KEP agrees with the scaling relation KEP ∝ (τacc/τdis)·φ/(1 − φ) with an error < 2%. All results are based on one-dimensional modeling using the method of characteristics with an effective wave speed c = 910 m/s, accounting for fluid–structure interaction and compliance due to the presence of gas [2, 9, 18]. The analysis is consistent with the law of energy conservation and with the classical theory of transient flows in pipelines.