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Non-Newtonian fluid flows experience turbulent regime in some industrial applications. Several approaches have been proposed for numerical simulation of turbulent flows that each one has specific features. RANS turbulence models have reasonable computational costs, while include several sources of uncertainties affecting simulation results. In addition, developed RANS models for non-Newtonian fluids are modified versions of available models for Newtonian fluids, therefore, they cannot provide reliable estimation for viscoplastic stress term. On the contrary, DNS delivers accurate results but with high computational costs. Consequently, use of DNS data for estimation of uncertainty in RANS models can provide better decision making for engineers based on RANS results. In the present study, a turbulence model based on for power-law non-Newtonian fluid is developed and employed for simulation of flow in a pipe. Then, an efficient method is proposed for quantification of available model-form uncertainty. Moreover, it is assumed that uncertainties originating from various sources are combined together in calculation of Reynolds stress as well as viscoplastic stress. Deviation of the stresses, computed using RANS turbulence model, from DNS data are modeled through Gaussian Random Field. Thereafter, Karhunen-Loeve expansion is employed for uncertainty propagation in simulation process. Finally, the effects of these uncertainties on RANS results are shown in velocity field demonstrating the fact that the presented approach is accurate enough for statistical modeling of model-form uncertainty in RANS turbulence models.

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In the present paper, nondeterministic CFD has been performed using polynomial chaos expansion and Gram-Schmidt orthogonalization method. The Gram-Schmidt method has been used in the literature for constructing orthogonal basis of polynomial chaos expansion in the projection method. In the present study, for the first time the Gram-Schmidt method is used in regression method. For the purpose of code verification, the output numerical basis of code for uniform and Gaussian probability distribution functions is compared to their corresponding analytical basis. The numerical method is further validated using a classical challenging function. Comparison of numerical and analytical statistics shows that developed numerical method is able to return reliable results for statistical quantities of interest. Subsequently, the problem of stochastic heat transfer in a grooved channel was investigated. The inlet velocity, hot wall temperature and fluid conductivity were considered uncertain with arbitrary probability distribution functions. The UQ analysis was performed by coupling the UQ code with a CFD code. The validity of numerical results was evaluated using a Monte-Carlo simulation with 2000 LHS samples. Comparison of polynomial chaos expansion and Monte-Carlo simulation results reveals an acceptable agreement. In addition a sensitivity analysis was carried out using Sobol indices and sensitivity of results on each input uncertain parameter was studied.

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Uncertainty at experimental results usually adds to experimental data in the form of error bound. Since uncertainties at input parameters play an important part at the discrepancy between numerical and experimental results, considering uncertain parameters in comparison of numerical and experimental results would be logical. Electroosmotic flow is one of the cases which uncertainty quantification on its numerical simulation is necessary because of the presence of uncertain parameters. In this study, uncertainty quantification of electroosmotic flow in the micro T-channel has been presented. Numerical method was first validated by comparison between numerical simulation results of electroosmotic flow with certain inputs and experimental data. At the first step of uncertainty quantification, sample generation of the uncertain parameters has been performed by Latin hypercube method. At the next step, governing equation of electroosmotic flow has been solved by finite element method for every sample. Mass flow rate and velocity field have been selected as objective functions and adjoint method was employed for calculating the derivatives of them. At the final stage uncertainty quantification has been performed by enhanced Monte Carlo method. Results of the adjoint method show geometry parameters and fluid viscosity as the most effective factors on the results. While temperature and density of fluid demonstrate the least effect on the objective functions. Results of the Monte Carlo method illustrate 22.4% uncertainty for the results of mass flow rate and 12.6% on average for the results of velocities.