An assessment of the thermal impact on the valve torque on cryogenically sub-zero temperatures


 A common challenge faced by valve designers for cryogenics is the prediction, evaluation, and conclusion of the most optimum design of the valve hand-wheel due to the enhanced torque required for the valve to operate at sub-zero temperatures. The research efforts are directed towards technical assessment to establish a correlation between the thermal variations and torque values for the valve. The research envisioned an experimental study conducted on Liquid Nitrogen (LIN) Media on an isolation type globe valve of the size of Diameter nominal 15mm on variable pressure value from 1 MPa to 3 MPa with temperature inception from -150 ºC (123 K) to -200 ºC (73 K). The experiment is modeled using the design of experiments methodology subsequently compared with the engineering design analytical methodology to correlate the two methods .


INTRODUCTION
So-called Permanent gases (also called as cryogens) such as Helium, Hydrogen, Argon, Nitrogen, Oxygen etc. are being liquefied in order to felicitate their transportation and storage due to less space and volume occupied post liquefaction. However, the challenge faced by industrialists and researchers constitutes the drawing off the gases from the cryogenic transport or storage tank with the required pressure and flow parameters. Therefore, the drawing off line of the cryogenic tanks are mounted with valves such as the ball, globe, check, safety valves etc. While the design seems very convenient for the hand-wheel operated isolation type globe and ball valves, the designer faces many difficulties in predicting, evaluating and concluding the most optimum design of the valve hand-wheel due to the enhanced torque required for the valve to operate at sub-zero temperatures. Currently, the designer is completely dependent on actual torque test on test bench post prototype development.
The research effort directs to analyze and study the behavioral pattern of torque of a cryogenic globe valve under different cryogenic conditions. It would be conducted on designed experiments methodology after monitoring the torque as response with pressure and temperature as varying factors at different levels. The methodology also involves comparing the experiments analytically for evaluating torque for cryogenic globe valves. The results will help the valve designer taking informed decision over predicting the torque the valve may generate (which is currently very difficult and completely dependent on actual torque test on test bench post prototype development).

Methodology
A designed experiment, Montgomery [1], is a test or series of tests in which purposeful changes are made to the input variables of a process so that we may observe and identify corresponding changes in the output response. The process can be visualized as some combination of machines, methods, and people that transforms an input material into an output product. This output product has one or more observable quality characteristics or responses. Some of the process variables x1, x2, . . ., xp are controllable, whereas others z1, z2, . . ., zq are uncontrollable (although they may be controllable for purposes of the test). For the design of the cryogenic globe valve, operating pressure and temperature are considered to be the controllable factors in the designed experiments. Uncontrollable factors considered includes coefficient of friction depending on material, surface finish and the manufacturing process and the valve port area which is constant for any two same size globe valves. The experiment to be designed shall be full factorial design with 2 factors, each on 5 levels with 2 replicas of observation during experiments. Since the number of factors are pragmatic, the model would be fixed effects model. The observations from a two-factor factorial experiment may be described by the model:

Statistical analysis
Generally, let Yi denote the total of all observations under ith level of factor A, Yj denote the total of all observations under the jth level of factor B, Yij denote the total of all observations in the ijth cell, and Y denote the grand total of all observations. Define ̅ , ̅̅̅ , ̅̅̅̅ , ̅ as the corresponding row, column, cell and grand averages. Expressed mathematically, The total corrected sum of squares may be written as This equation symbolically may be written as following Each sum of squares divided by its degrees of freedom is a mean square. The expected values of the mean squares are

Sum of Squares
Degrees of freedom The experiment involves using two cryogenic tanks: one stationary and one mobile. After conducting the experiments, the data points are analyzed using statistical methods and analysis of variance is done. The tool used is Minitab 19 [3]. Uncertainty analysis and confidence interval is done at interval of 95% confidence.

Interpretation of results
In this study, design of experiments was used as a statistical method for assessing the influence of critical process parameters on the output/response of opening torque for the DN15 Cryogenic Globe valve. For this purpose, full factorial design of two factors at five levels was built. The effect of the main factors and their interaction on the response was evaluated using regression analysis, analysis of variance and graphical analysis of the experimental design. A matrix of full factorial design on the represented 2 factors at five levels was built    , regarding the general model, we noted the following important  characteristic Temperature 103 K, interactive factors 14 110, 14 113, 17 103, 22 110, 22 113, 25 103, 25 113 looks less significant as P-value for these combinations is greater than 0.05. The coefficient of determination R², which shows the proportional variation in the response explained by independent variables in the linear regression model is 0.9988 and the adjusted coefficient of determination is 0.9977. The value of R² is close to 1 reveals that there is considerable linear relationship between the factors and the response. The value of R² demonstrates that with more than 99 % confidence the change in response can be explained with the variables in the model. There is some slight difference between R² and R² adj values, which shows that some insignificant conditions were included in the model.

ANALYTICAL APPROACH
As per the analytical methodology, torque, Q, required to affect the valve closure is addition of , , and , Pearson [2] where = torque required to impart the total axial force generated by pressure at valve inlet = torque required to overcome the frictional resistance to rotate the spindle = torque required to overcome the resistance by the gland packing grip

DISCUSSIONS
The reader may observe that net opening torque is principally the addition of and and the globe valve considered possess under-the-plug flow design which do not oppose the pressure inlet. Among the three types, torque required to overcome friction between spindle and threaded bush is the highest. It also increases with the pressure value at the valve inlet. For instance, there is an increase of around 37 % of the total torque required when pressure increased from 22 Kg/cm² (2.15 MPa) to 30 kg/cm² (2.94 MPa) at same temperature. The reason being the frictional surface contact within the two metal parts (spindle and threaded bush) with coefficient of friction equals 0.40. Total experimental torque required to overcome the net frictional force for 22 Kg/cm² (2.15 MPa) at 110 K is 2.88 Nm which increases to 3.28 Nm at same temperature. However, the experimental values of net torque decrease by few percentages when the temperature is increased which reasons for the relieving in the thermal stresses which may have developed relatively lower temperature. The analytical calculations and valve design are driven by the Maximum allowable working pressure, MAWP, of the industrial process and the pipeline on which these valves would be mounted. Since the MAWP is 5 MPa, therefore the valve design is holistically designed analytically on 5 MPa. Juxtaposing analytical with experimental values of net opening torque at cryogenic conditions, it is observed that experimentally torque values are higher than analytical values by factor of 1.67 for 22 Kg/cm² (2.15 MPa) and 0.40 for 30 Kg/cm² (2.94 MPa) respectively. As mentioned in the earlier text, the reader may identify that the Handwheel diameter is designed not only to justify the analytical values of torque. Its design is also not limited to assumptions that the torque values at cryogenic temperatures may be greater than what analytically calculated at ambient conditions. The design of the handwheel is assumed to bear the rising torque in case there are some foreign particles inside the threads between the spindle and the threaded bush which thereby increases the overall frictional contact area. The effect seen on overall torque with the frictional torque at thread area (Spindle /threaded bush) is the largest.

FUTURE WORK
The future scope of the project lies in numerical methodologies to correlate the experimental and analytical approach to help the valve designer to take informed decision with the optimized cost. Also, the future research scope envisaged to reduce and nullify the assumptions considered which includes coefficient of friction to surface roughness analysis. Another approach could be is to study the correlation between thermal gradient developed due to actual surface roughness.