GS
G.O. Schreuder
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Large-scale liquid hydrogen storage motivates non-vacuum insulation concepts for double-walled storage tanks in which rigid polyurethane foam is bonded directly to the inner steel shell, behind a passive perlite layer. During filling of the tank with liquid hydrogen, the insulation material is cooled from ambient temperature towards 20 Kelvin, at which hydrogen liquefies at atmospheric pressure. Cracking sounds reported during laboratory thermal cycling, predominantly on warm-up, suggest potential mechanical failure of the polyurethane insulation material. The mechanical integrity is therefore a governing design concern, yet the stress and elastic strain developing within the polyurethane foam during these temperature transients remain insufficiently quantified.
This thesis investigates how transient thermal gradients and constrained thermal contraction generate stress and elastic strain concentrations in bonded cryogenic foam insulation. A coupled transient thermo-mechanical finite element model was built in ANSYS Mechanical APDL, using an axisymmetric formulation for a homogenised, isotropic, linear elastic foam with temperature-dependent conductivity and stiffness, and thermal contraction referenced to the stress-free state at 293 Kelvin. Three configurations were analysed, progressing from an idealised foam–steel corner geometry to an experiment-specific assembly and a spherical tank model, so that the simplest model provides a reference for the more complex ones.
The cold region was driven from 293 Kelvin to 20 Kelvin along a smooth, monotonically decreasing ramp, held cold and warmed to 100 Kelvin, with cooling-rate, cooling-path, warm-up-rate and material-property sensitivity cases. The mechanical formulation is linear elastic and contains no damage law: failure is assessed in a separate post-processing step, so the results are risk indicators rather than validated failure predictions. Within that scope, the model does identify where and when cracking is most likely, through two criteria: the first principal stress against the cryogenic tensile strength, and the first principal elastic strain against the strain-to-failure.
The strain criterion governs, and it localises the risk to the bonded foam–steel interface and its geometric discontinuities at the end of cool-down. Two mechanisms produce this loading. The first is a stationary tensile concentration at the foam-steel interface, whose stress magnitude is set by the product of foam stiffness, expansion mismatch and total temperature drop, and locally amplified at the corner. The second is an internal tensile peak that travels outward with the cooling front and is largest at the end of cool-down.
The mismatch sets the amplitude of both the interface concentration and the internal peak, whereas the foam stiffness scales only the stress and leaves the elastic strain unchanged, making the problem strain-controlled. The severity then depends on the accumulated temperature drop rather than on the cooling path: neither slower nor stepwise cooling reduced the peaks, and warm-up peaks nowhere substantially exceeded cool-down at matched cold-side temperatures. Both features also persist in the corner-free spherical tank.
Reducing the foam-substrate expansion mismatch is therefore a more effective mitigation than adjusting the cooling protocol. The observed warm-up cracking cannot be reproduced by an elastic model and most plausibly reflects history-dependent damage initiated at the cold state. Future work should add a cohesive-zone formulation and characterise the foam down to 20 Kelvin. ...
This thesis investigates how transient thermal gradients and constrained thermal contraction generate stress and elastic strain concentrations in bonded cryogenic foam insulation. A coupled transient thermo-mechanical finite element model was built in ANSYS Mechanical APDL, using an axisymmetric formulation for a homogenised, isotropic, linear elastic foam with temperature-dependent conductivity and stiffness, and thermal contraction referenced to the stress-free state at 293 Kelvin. Three configurations were analysed, progressing from an idealised foam–steel corner geometry to an experiment-specific assembly and a spherical tank model, so that the simplest model provides a reference for the more complex ones.
The cold region was driven from 293 Kelvin to 20 Kelvin along a smooth, monotonically decreasing ramp, held cold and warmed to 100 Kelvin, with cooling-rate, cooling-path, warm-up-rate and material-property sensitivity cases. The mechanical formulation is linear elastic and contains no damage law: failure is assessed in a separate post-processing step, so the results are risk indicators rather than validated failure predictions. Within that scope, the model does identify where and when cracking is most likely, through two criteria: the first principal stress against the cryogenic tensile strength, and the first principal elastic strain against the strain-to-failure.
The strain criterion governs, and it localises the risk to the bonded foam–steel interface and its geometric discontinuities at the end of cool-down. Two mechanisms produce this loading. The first is a stationary tensile concentration at the foam-steel interface, whose stress magnitude is set by the product of foam stiffness, expansion mismatch and total temperature drop, and locally amplified at the corner. The second is an internal tensile peak that travels outward with the cooling front and is largest at the end of cool-down.
The mismatch sets the amplitude of both the interface concentration and the internal peak, whereas the foam stiffness scales only the stress and leaves the elastic strain unchanged, making the problem strain-controlled. The severity then depends on the accumulated temperature drop rather than on the cooling path: neither slower nor stepwise cooling reduced the peaks, and warm-up peaks nowhere substantially exceeded cool-down at matched cold-side temperatures. Both features also persist in the corner-free spherical tank.
Reducing the foam-substrate expansion mismatch is therefore a more effective mitigation than adjusting the cooling protocol. The observed warm-up cracking cannot be reproduced by an elastic model and most plausibly reflects history-dependent damage initiated at the cold state. Future work should add a cohesive-zone formulation and characterise the foam down to 20 Kelvin. ...
Large-scale liquid hydrogen storage motivates non-vacuum insulation concepts for double-walled storage tanks in which rigid polyurethane foam is bonded directly to the inner steel shell, behind a passive perlite layer. During filling of the tank with liquid hydrogen, the insulation material is cooled from ambient temperature towards 20 Kelvin, at which hydrogen liquefies at atmospheric pressure. Cracking sounds reported during laboratory thermal cycling, predominantly on warm-up, suggest potential mechanical failure of the polyurethane insulation material. The mechanical integrity is therefore a governing design concern, yet the stress and elastic strain developing within the polyurethane foam during these temperature transients remain insufficiently quantified.
This thesis investigates how transient thermal gradients and constrained thermal contraction generate stress and elastic strain concentrations in bonded cryogenic foam insulation. A coupled transient thermo-mechanical finite element model was built in ANSYS Mechanical APDL, using an axisymmetric formulation for a homogenised, isotropic, linear elastic foam with temperature-dependent conductivity and stiffness, and thermal contraction referenced to the stress-free state at 293 Kelvin. Three configurations were analysed, progressing from an idealised foam–steel corner geometry to an experiment-specific assembly and a spherical tank model, so that the simplest model provides a reference for the more complex ones.
The cold region was driven from 293 Kelvin to 20 Kelvin along a smooth, monotonically decreasing ramp, held cold and warmed to 100 Kelvin, with cooling-rate, cooling-path, warm-up-rate and material-property sensitivity cases. The mechanical formulation is linear elastic and contains no damage law: failure is assessed in a separate post-processing step, so the results are risk indicators rather than validated failure predictions. Within that scope, the model does identify where and when cracking is most likely, through two criteria: the first principal stress against the cryogenic tensile strength, and the first principal elastic strain against the strain-to-failure.
The strain criterion governs, and it localises the risk to the bonded foam–steel interface and its geometric discontinuities at the end of cool-down. Two mechanisms produce this loading. The first is a stationary tensile concentration at the foam-steel interface, whose stress magnitude is set by the product of foam stiffness, expansion mismatch and total temperature drop, and locally amplified at the corner. The second is an internal tensile peak that travels outward with the cooling front and is largest at the end of cool-down.
The mismatch sets the amplitude of both the interface concentration and the internal peak, whereas the foam stiffness scales only the stress and leaves the elastic strain unchanged, making the problem strain-controlled. The severity then depends on the accumulated temperature drop rather than on the cooling path: neither slower nor stepwise cooling reduced the peaks, and warm-up peaks nowhere substantially exceeded cool-down at matched cold-side temperatures. Both features also persist in the corner-free spherical tank.
Reducing the foam-substrate expansion mismatch is therefore a more effective mitigation than adjusting the cooling protocol. The observed warm-up cracking cannot be reproduced by an elastic model and most plausibly reflects history-dependent damage initiated at the cold state. Future work should add a cohesive-zone formulation and characterise the foam down to 20 Kelvin.
This thesis investigates how transient thermal gradients and constrained thermal contraction generate stress and elastic strain concentrations in bonded cryogenic foam insulation. A coupled transient thermo-mechanical finite element model was built in ANSYS Mechanical APDL, using an axisymmetric formulation for a homogenised, isotropic, linear elastic foam with temperature-dependent conductivity and stiffness, and thermal contraction referenced to the stress-free state at 293 Kelvin. Three configurations were analysed, progressing from an idealised foam–steel corner geometry to an experiment-specific assembly and a spherical tank model, so that the simplest model provides a reference for the more complex ones.
The cold region was driven from 293 Kelvin to 20 Kelvin along a smooth, monotonically decreasing ramp, held cold and warmed to 100 Kelvin, with cooling-rate, cooling-path, warm-up-rate and material-property sensitivity cases. The mechanical formulation is linear elastic and contains no damage law: failure is assessed in a separate post-processing step, so the results are risk indicators rather than validated failure predictions. Within that scope, the model does identify where and when cracking is most likely, through two criteria: the first principal stress against the cryogenic tensile strength, and the first principal elastic strain against the strain-to-failure.
The strain criterion governs, and it localises the risk to the bonded foam–steel interface and its geometric discontinuities at the end of cool-down. Two mechanisms produce this loading. The first is a stationary tensile concentration at the foam-steel interface, whose stress magnitude is set by the product of foam stiffness, expansion mismatch and total temperature drop, and locally amplified at the corner. The second is an internal tensile peak that travels outward with the cooling front and is largest at the end of cool-down.
The mismatch sets the amplitude of both the interface concentration and the internal peak, whereas the foam stiffness scales only the stress and leaves the elastic strain unchanged, making the problem strain-controlled. The severity then depends on the accumulated temperature drop rather than on the cooling path: neither slower nor stepwise cooling reduced the peaks, and warm-up peaks nowhere substantially exceeded cool-down at matched cold-side temperatures. Both features also persist in the corner-free spherical tank.
Reducing the foam-substrate expansion mismatch is therefore a more effective mitigation than adjusting the cooling protocol. The observed warm-up cracking cannot be reproduced by an elastic model and most plausibly reflects history-dependent damage initiated at the cold state. Future work should add a cohesive-zone formulation and characterise the foam down to 20 Kelvin.