ASEE Southeast Section Conference INTEGRATING MODEL VALIDATION AND UNCERTAINTY ANALYSIS INTO AN UNDERGRADUATE ENGINEERING LABORATORY W. G. Steele and J. A. Schneider Department of Mechanical Engineering Bagley College of Engineering Mississippi State University Mississippi State, MS 39762

INTRODUCTION MS STATE LABORATORY COURSES METHODOLOGY EXAMPLE CONCLUSION

INTRODUCTION Laboratories introduce the student to the use of various measurement devices along with the associated experimental uncertainties Theoretical engineering models are used to compare predicted outcome with the experimental results Usually no consideration of the uncertainty associated with the theoretical model calculations Concept of engineering model validation using uncertainty analysis is extension of verification and validation research for CFD and other computational design codes

MS STATE LABORATORY COURSES Experimental Orientation basic measurements data acquisition concepts of uncertainty analysis Experimental Techniques I experiment design using uncertainty analysis experiment operation Experimental Techniques II model, plan, design, construct, operate, and analyze results of an experiment including model validation

Consider a validation comparison: E U r m ± U m X riri mimi m  value from the model r  result from experiment E  comparison error E = r - m =  r -  m

Validation Comparison of Model Results with Experimental Results

METHODOLOGY The comparison error has an uncertainty If is less than U E, the level of model validation is U E. If is greater than U E, the level of model validation is.

For the experimental result the uncertainty is where b r = systematic standard uncertainty s r = random standard uncertainty

The systematic standard uncertainty of the result is defined as where and where B i is the 95% confidence estimate (2b i ) of the limits of the true systematic error for variable X i. The random standard uncertainty of the result is defined as

For the model result the uncertainty is

EXAMPLE Experiment result was the measured head loss in a pipe,  hp r, over a range of flow rates. Engineering model was where and

Fluid Flow Test Facility

Experimental Results vs. Model Predictions

Variable Value Systematic Standard Uncertainty Random Standard Uncertainty pipe head loss (  hp r ) Variable0.141 in0.04 in orifice head loss (  ho) Variable0.05 in0.08 in pipe length (L) in0.031 in- pipe diameter (d)0.697 in in- flow coefficient (C)11.45 in 2.5 /sec0.089 in 2.5 /sec- roughness (  ) 3.6X10 -6 in50%- water density (  ) 999 kg/m 3 0.3%- water viscosity (  ) 1.056X10 -3 Nsec/m 2 7%- Uncertainty Estimates for Result and Model Variables

Comparison Error

Uncertainty Percentage Contributions Variable Reynolds Number 22,62348,279 Systematic Standard Uncertainty Random Standard Uncertaint y Systematic Standard Uncertainty Random Standard Uncertainty pipe head loss (  hp r ) orifice head loss (  ho) pipe length (L) pipe diameter (d) flow coefficient (C) roughness (  ) water density (  ) water viscosity (  ) Sum = 100.0

CONCLUSION Understanding the limitations of physical models is key to the successful practice of engineering. The uncertainty of both the model and experiment results are used to assess the model validity. The validation process allows the identification of ranges where different or improved models are needed or shows that improved variable uncertainties are needed to reduce the validation uncertainty.