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DEVELOPMENT OF AN ULTRA-HIGH EFFICIENCY GAS TURBINE ENGINE (UHEGT

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DEVELOPMENT OF AN ULTRA-HIGH EFFICIENCY GAS TURBINE ENGINE (UHEGT ( development-an-ultra-high-efficiency-gas-turbine-engine-uheg )

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In which the index k refers to the axial position at Δ𝑋/2. Equation of Motion: The equation of momentum in the index notation is described as, In which the divergence of shear stress tensor ∇ ∙ 𝑇 = 𝑒 𝜕𝑇 /𝜕𝑥 represents the shear 𝑖 𝑖𝑗 𝑗 force acting on the surface of the element. In a one-dimensional flow, the only non-zero term is related to the wall shear stress 𝜏𝑤 that can be expressed in terms of friction coefficient cf as, 𝜏 =𝑐𝜌𝑉2 (6.5) 𝑤𝑓2 Considering that the shear stress is zero outside of the boundary layer, and by replacing Δ𝑦 by the characteristic length hydraulic diameter Dh, after inserting all variables and simplification, the momentum equation for a discretized domain will be approximated as [1], (6.6) 𝜕(𝜌𝑉)𝜕 𝜕𝑝𝜕𝑇 𝑖 = − (𝜌𝑉 𝑉 ) − + 𝑖𝑗 (6.4) 𝜕𝑡 𝜕𝑥 𝑖𝑗 𝜕𝑥 𝜕𝑥 𝑗𝑖𝑗 𝜕𝑚̇𝑘=−1(𝑚̇ 𝑉 −𝑚̇𝑉+𝑝 𝑆 −𝑝𝑆) 𝜕𝑡 Δx 𝑖+1 𝑖+1 𝑖 𝑖 𝑖+1 𝑖+1 𝑖 𝑖 𝑚̇2 𝑆𝑘 Δ𝑥 𝑓 2𝐷h𝑘𝜌𝑘𝑆𝑘 𝑚̇𝑉+𝑃𝑆 𝑆 −𝑆 +( 𝑘 𝑘 𝑘 𝑘)(𝑖+1 𝑖)−𝑐 𝑘 The Energy Equation: The energy equation can be expressed in terms of total enthalpy H in index notation as, 118

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