Analytical Model for Cryogenic Stratification in a Rotating and Reduced-Gravity Environment

Oliveira, Justin; Kirk, Daniel; Schallhorn, Paul

doi:10.2514/1.39760

Cited by 17 publications

(16 citation statements)

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“…Modeling of propellant thermal stratification requires an understanding of the mechanisms by which mass and energy are transported within the tank. The principal mechanism is buoyancyinduced natural convection, which is initiated by solar heating of the tank walls [1][2][3][4][5]. A schematic of thermal stratification occurring within a propellant tank is shown in Fig.…”

Section: A Overview Of Thermal Stratification In Rocket Propellant Tmentioning

confidence: 99%

“…Additionally, the ullage pressure rise associated with a thermally stratified tank is greater than the pressure rise associated with the cryogenic fluid mixed at uniform temperature, leading to tank overpressurization and prevention venting of gaseous propellant, which is especially relevant for the self-pressurizing LH 2 . Additional detailed descriptions of thermal stratification within rocket propellant tanks can be found in [1][2][3][4][5].…”

Section: A Overview Of Thermal Stratification In Rocket Propellant Tmentioning

confidence: 99%

“…The temperature difference θ w is defined as the difference between the wall temperature T w and the fluid bulk temperature T b . During the low acceleration coast typically associated with upper stages and heat loads shown in Table 1, the buoyancy-driven free convection boundary layer on the inner tank walls is typically laminar [1]. In contrast, for propellant stratification situations that arise when the vehicle is on the launch pad (where both Ra and Ra are orders of magnitude above transition), the wall boundary layers are predominantly turbulent.…”

Section: Ra Grprmentioning

confidence: 99%

“…(3)(4)(5)(6)(7)(8) are for smooth walls. More details regarding the use of the boundary-layer equations for prediction of the thermal stratification layer growth and temperature as well as the analogous correlations for cases of constant wall heat flux are given in [1][2][3][4][5].…”

Section: Ra Grprmentioning

confidence: 99%

“…Propellant thermal stratification models have been developed to provide mission planners with tools to obtain estimates for propellant temperature at the conclusion of a low-acceleration coast between two orbits [1][2][3][4][5]. Analytical propellant stratification models are based on buoyancy-driven free convection velocity and temperature correlations developed for flow along smooth vertical walls.…”

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confidence: 99%

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Effect of Isogrid-Type Obstructions on Thermal Stratification in Upper-Stage Rocket Propellant Tanks

Faure

Oliveira

Chintalapati

et al. 2014

Journal of Spacecraft and Rockets

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Analytical models for propellant thermal stratification are typically based on smooth wall flow correlations. However, many propellant tank walls have a mass-saving isogrid, which alters the boundary layer. This work investigates the boundary-layer behavior over walls with obstruction elements that are representative of isogrid or internal stiffener rings. The experimental studies reveal that the thickness of the velocity boundary layer over an isogrid wall is more than 200% thicker than a smooth wall at full-scale upper-stage tank Reynolds numbers. For buoyancy-induced free convection flows, the computational-fluid-dynamics models demonstrate that the velocity boundary layer over a wall lined with obstruction elements may be thicker or thinner than the equivalent boundary layer over a smooth wall, whereas the thermal boundary layer is always thicker for the rough wall. A Rayleigh number scaling analysis is presented for a range of fluids, tank and obstruction sizes, heat loads, and acceleration levels. When the results are applied to a full-scale liquid-hydrogen tank with obstruction elements, the stratification layer is 18% thicker, and the stratum fluid is 31% warmer than the corresponding results for the smooth wall tank. The increase is attributable to the augmented heat transfer area and enhanced mixing of fluid due to the obstruction element. Nomenclature c p = specific heat at constant pressure, J∕kg · K Gr = Grashof number (based on temperature difference) Gr = modified Grashof number (based on heat flux) g = local gravitational acceleration, m∕s 2 H = initial liquid fill level, m h = obstruction height, m L = tank height, m l = length between obstruction, m _ m = mass flow rate, kg∕s N = number of obstruction elements Nu = Nusselt number P = pressure, N∕m 2 Pr = Prandtl number _ q = heat flux, W∕m 2 R = tank radius, m Ra = Rayleigh number (based on temperature difference) Ra = modified Rayleigh number (based on heat flux) Re = Reynolds number S = run length along the obstruction elements, m s = obstruction element center-to-center spacing distance, m t = time, s; or isogrid element thickness, m U, u = velocity, m∕s x, y, z = length, m α = thermal diffusivity, m 2 ∕s β = volumetric thermal expansion coefficient, 1∕K Δ = thickness of stratified layer, m δ = 99% of U e boundary-layer thickness, m δ = boundary-layer displacement thickness, m ε = obstruction parameter ζ = nondimensional velocity η = yU e ∕νx 1∕2 , nondimensional boundary-layer variable θ = temperature difference between wall and fluid, K; or boundary-layer momentum thickness, m κ = thermal conductivity, W∕m · K μ = dynamic viscosity, N · s∕m 2 ν = kinematic viscosity, m 2 ∕s ξ = nondimensional temperature ρ = density, kg∕m 3 τ = implicit time step, s χ = boundary-layer energy flow rate, J∕s ω = spacecraft rotational spin rate, deg ∕s Subscripts b = bulk fluid bl = boundary layer e = external to boundary layer s = stratum td = touchdown distance behind backward-facing step trans = laminar to turbulent boundary-layer transition distance u = ul...

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