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ABSTRACT
Methane heat-transfer deterioration can occur in the regenerative cooling channels of future liquid-oxygen/liquid-methane rocket engines with chamber pressures higher than about 50 bar. Aiming to improve the prediction capabilities for the design of such systems, in the present study, a Nusselt number correlation able to describe the convective heat-transfer characteristics of supercritical flow exhibiting deterioration and with negligible buoyancy effects is obtained using data from numerical simulations. The adopted numerical solver of the Navier–Stokes equations is first validated against the experimental data of near-critical hydrogen in heated tubes and then used to collect heat-transfer data of supercritical methane in a heated tube for different levels of pressure, temperature, and mass flux.
Nomenclature
| 𝒜 | = | error amplification |
| 𝒦 | = | turbulent kinetic energy, [m2/s2] |
| = | mass flow rate, [kg/s] | |
| ℜ | = | thermal resistance, [m2K/W] |
| A | = | tube cross section area, [mm2] |
| cp | = | specific heat at constant pressure, [J/g K] |
| cv | = | specific heat at constant volume, [J/g K] |
| D | = | tube diameter, [mm] |
| fw | = | skin friction coefficient |
| G | = | mass flux, [kg/m2s] |
| g | = | gravity acceleration, [m/s2] |
| h | = | enthalpy, [J/g] |
| hc | = | heat transfer coefficient, [W/m2K] |
| k | = | thermal conductivity, [W/m K] |
| Kr | = | buoyancy parameter |
| L | = | tube length, [mm] |
| Nu | = | Nusselt number |
| P | = | tube cross section perimeter, [mm] |
| p | = | pressure, [bar] |
| = | probability density function | |
| Pr | = | Prandtl number |
| qw | = | heat flux, [MW/m2] |
| R | = | tube radius, [mm] |
| r | = | radial axis, [mm] |
| Re | = | Reynolds number |
| T | = | temperature, [K] |
| u | = | axial velocity, [m/s] |
| v | = | radial velocity, [m/s] |
| x | = | tube axis, [mm] |
| α | = | thermal expansion, [1/K] |
| β | = | isothermal compressibility, [1/bar] |
| δ | = | thickness, [mm] |
| η | = | distance from wall, [mm] |
| Λ | = | Nusselt number correction factor |
| μ | = | dynamic viscosity, [Pa s] |
| ρ | = | density, [mol/l] |
| τ | = | shear stress, [bar] |
| ϵ | = | error |
| Subscripts | = | |
| b | = | bulk |
| c | = | critical |
| e | = | exit |
| i | = | inflow |
| m | = | molecular |
| pc | = | pseudo-critical |
| t | = | turbulent |
| v | = | viscous sublayer |
| w | = | wall |
| Acronyms | = | |
| CFD | = | Computational Fluid Dynamics |
Nomenclature
| 𝒜 | = | error amplification |
| 𝒦 | = | turbulent kinetic energy, [m2/s2] |
| = | mass flow rate, [kg/s] | |
| ℜ | = | thermal resistance, [m2K/W] |
| A | = | tube cross section area, [mm2] |
| cp | = | specific heat at constant pressure, [J/g K] |
| cv | = | specific heat at constant volume, [J/g K] |
| D | = | tube diameter, [mm] |
| fw | = | skin friction coefficient |
| G | = | mass flux, [kg/m2s] |
| g | = | gravity acceleration, [m/s2] |
| h | = | enthalpy, [J/g] |
| hc | = | heat transfer coefficient, [W/m2K] |
| k | = | thermal conductivity, [W/m K] |
| Kr | = | buoyancy parameter |
| L | = | tube length, [mm] |
| Nu | = | Nusselt number |
| P | = | tube cross section perimeter, [mm] |
| p | = | pressure, [bar] |
| = | probability density function | |
| Pr | = | Prandtl number |
| qw | = | heat flux, [MW/m2] |
| R | = | tube radius, [mm] |
| r | = | radial axis, [mm] |
| Re | = | Reynolds number |
| T | = | temperature, [K] |
| u | = | axial velocity, [m/s] |
| v | = | radial velocity, [m/s] |
| x | = | tube axis, [mm] |
| α | = | thermal expansion, [1/K] |
| β | = | isothermal compressibility, [1/bar] |
| δ | = | thickness, [mm] |
| η | = | distance from wall, [mm] |
| Λ | = | Nusselt number correction factor |
| μ | = | dynamic viscosity, [Pa s] |
| ρ | = | density, [mol/l] |
| τ | = | shear stress, [bar] |
| ϵ | = | error |
| Subscripts | = | |
| b | = | bulk |
| c | = | critical |
| e | = | exit |
| i | = | inflow |
| m | = | molecular |
| pc | = | pseudo-critical |
| t | = | turbulent |
| v | = | viscous sublayer |
| w | = | wall |
| Acronyms | = | |
| CFD | = | Computational Fluid Dynamics |