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Finite Element Analysis (FEA)
For the design of the HIP pressure vessel, it was critical to assess the performance of the chamber through a pressure simulation using FEA software. The simulations were meant to assess the factor of safety, the stresses, and the strains on the current pressure vessel design at the targeted operating pressure of 15,000 psi. Utilizing Fusion 360 FEA software, the performance of our current design was assessed using simplified models of the pressure vessel design as we desired to get a general sense of how the overall pressure vessel shell, dimensions, and material selection would fair under extremely high pressures.
For the following results below, the simulations were done with pressure vessel componenets being being composed of Inconel 718, with 5 inch wall thickness. The simulations were done using 15,000 psi as the pressure load and the images portray the stress results of the simulations with the scales on the left being in units of psi.
Overall Pressure Vessel Shell.
Overall Pressure Vessel Shell.
Cylindrical Shell and Center Column.
Cylindrical Shell and Center Column.
Pressure Vessel Lid.
Pressure Vessel Lid.
FEA Results
The results of the FEA are promising. It is observed that there are very minimal stress concentrations in the design. The stress concentrations that do exist, marked by regions of dark red, in all three results are likely not due to the design of the components, but largely due to how the models were constrained.
The overall factor of safety result of the simulation for the overall pressure vessel shell came out to be around 2. This is a positive result for our current design, but with further iterations and work it can and it must be improved, as the industry standard for FEA simulations typically range from 3.5-4.
Heating Element
The current design iteration and idea for introducing the heating aspect of the HIP is to utilize heating rods within the pressure vessel. The idea is to line the heating rods along the inside perimeter of the inner pressure vessel to introduce uniform heat distribution.
To assess the feasibility of the heating rods, we had to figure out the rate of heat transfer the heating rods would produce and how much it would cost to heat the rods.
For the current rods design, it was decided that we would use 1 inch diameter stainless steel heating rods and with these details decided, the heat transfer and cost was also determined.
Stainless Steel Heating Rod Design.
Heating Calculations
Heat transfer and cost was determined using Fourier's law of heat conduction, which states that the rate of heat transfer through a material is proportional to the negative gradient of temperature and the cross-sectional area of the material.
Mathematically, it can be represented as: Q = -kA * (dT/dx). Where: Q is the rate of heat transfer (in watts, W), k is the thermal conductivity of the material (in watts per meter per degree Celsius, W/(m°C)), A is the cross-sectional area of the rod (in square meters, m^2), and dT/dx is the temperature gradient along the rod (in degrees Celsius per meter, °C/m). Using one-inch stainless steel heating rods we would get Q = 6.93 Watts per heating rod. This means it would cost $0.00718 to run 1 heating element for the average HIP cycle of 180 minutes (about 3 hours).
HIP Controls System
An obvious design component for the HIP is the control system that will control the rate at which the pressure vessel is heated and pressurized, the cooling rate, and the hold time for the target temperature and pressure. Utilizing our current understanding of control theory, we designed a theoretical control system to modulate pressures and temperatures for a HIP. Due to time constraint, we focused our efforts towards replicating the heating and pressurizing stage of the HIP cycle and the holding stage, ignoring the rate of cooling.
Simulink divided into Each Functional Section: (1) the input, (2) calculation of dT/dt, (3) signal conversion into temperature, (4) signal conversion to pressure, (6) correction feedback loop of temperature, and (7) the time delay ( 0.1s).
Simulink Model
The controls model was designed and simulated via MATLAB-Simulink software. The current design of our control system to the left is modeled as a PID controller. The step block represents the heat input to the system and the target temperature value to hold for an extended period. The gain values (triangular blocks) represent the constants in the final theoretical model of temperature and the final conversion of the output temperature to pressure using .There is also the implementation of the time delay transfer function G(s) in (7) and the incorporation of the PID controller block (2) which is used to correct for the error during the HIP cycle. There is also the addition of a constant block to account for the initial environmental temperature and pressure assumed to be at STP.
Simulink Results
Realistic HIP cycle with temperature and pressure gain (increase) to target for soak time (plateau), followed by cooling phase (decrease).
Realistic HIP cycle with temperature and pressure gain (increase) to target for soak time (plateau), followed by cooling phase (decrease).
Pressure in blue (atm) and Temperature in yellow (K) vs. Time (min).
Pressure in blue (atm) and Temperature in yellow (K) vs. Time (min).
Our Simulink results do well to achieve the target pressure and temperature and to hold at those values as well. Current issues with the results are that the rise time is too fast and the overshoot is too large. With further work this can be refined.
Created by: Pouya Rassouli
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