Uncertainties exist in thermal-fluid systems in the form of manufacturing tolerances, design uncertainties, or measuring errors. These uncertainties could have a significant impact on the response variables of the system. There are various methods to assess this impact through uncertainty and sensitivity analyses.
Flownex SE has the capability to perform sensitivity analyses through either a parametric study or a Monte Carlo analysis.
The parametric study is the simplest, adjusting only one variable at a time through a user specified range, and hence it will provide results in the quickest time. The parametric study can be used to determine the variables with the largest influence on cycle parameters. By calculating the percentage change of input variables against the percentage change of cycle response variables, one can determine the sequence of importance of the different input parameters.
On the other hand, with the Monte Carlo analysis all nominated variables are varied simultaneously according to a model using random selections from a prescribed range and distribution.
In a parametric study, the response of the system is analyzed via nominated dependent (output) variables as a result of the sequential modification of nominated independent (input) variables. The input variables are varied one at a time through a range from a specified lower limit to a specified higher limit through a given number of increments. Each variable is reset to the nominal value before the next variable is analyzed.
A Monte Carlo analysis is defined as the simultaneous random variation of parameters to determine their combined impact on certain system responses. In contrast to the parametric study, perturbations for each variable are random rather than sequential and variables are perturbed simultaneously.
Examples of Parametric Studies
1. Pipeline Cost Evaluation
If we consider a pipeline that pumps water over 3km with an elevation of 300m the pipeline diameter will have a large influence on the pumping requirements and life cycle cost (LCC) of the system. To determine the optimum ratio between pipeline diameter, pumping power and LCC, a parametric study can be performed to sequentially vary the pipeline diameter. The parametric study results can be analyzed at the various sequential diameters and an optimum pipeline diameter can be selected.
2. Impact of pipeline connection tolerances
To perform a Monte Carlo study analysis on a typical pipeline connection as shown above, Flownex users can setup the sensitivity analysis tool to determine the effect of all the uncertainty ranges in the connection. The Monte Carlo solver will simultaneously and randomly vary between the tolerance ranges of all the specified variables to ensure maximum uncertainty bands are accounted for.
For the Monty Carlo analysis on a typical pipeline connection the following parameters can be taken into account:
- Variation in gasket position and its effect on the flow.
- Variation in piping roughness.
- Variation in upstream and downstream losses.
By taking into account the tolerance ranges the combined impact of all the uncertainties is account, evaluation of all connections on a complete pipeline system can highlight large variation in conditions due to system tolerances.
Impact of ambient conditions & system tolerances on cycle efficiency
A Monte Carlo study of the most influential components in a Rankine cycle allows engineers to determine the minimum and maximum influence the uncertainties have on the system efficiency.
Tolerances on Heat Exchanges, Turbines, Compressors, Material conduction, Insulation, etc. Are simultaneously and randomly varied to determine the maximum effect the combined uncertainties have on the system.