Nanofluids are regarded as an effective cooling medium with tremendous potential in heat transfer enhancement. In reality, nanofluids in microchannels are at the mercy of uncertainties unavoidably due to manufacturing error, dispersion of physical properties, and inconstant operating conditions. To obtain a deeper understanding of forced convection of nanofluids in microchannels, uncertainties are suggested to be considered. This paper studies numerically the uncertain forced convection of Al2O3-water nanofluid laminar flow in a grooved microchannel. Uncertainties in material properties and geometrical parameter are considered. The uncertainties are represented by interval variables. By employing Chebyshev polynomial approximation, interval method (IM) is presented to estimate the uncertain thermal performance and flow behavior of the forced convection problem. The validation of the accuracy and effectiveness of IM are demonstrated by a comparison with the scanning method (SM). The variation of temperature, velocity, and Nusselt number are obtained under different interval uncertainties. The results show that the uncertainties have remarkable influences on the simulated thermal performance and flow behavior.
The asymmetric rotor and the rub-impact behavior are important sources of instability and may cause severe vibrations. However, the dynamics of the rotor-bearing system simultaneously considering the two factors has not gained sufficient attention in available investigations. In this paper, the steady-state response and stability of an asymmetric rotor with rub-impact were evaluated. The asymmetric rotor was modeled by beam elements with asymmetric cross section, and the nonlinear equations of motion were established in the rotating frame. The multiharmonic balance (MHB) method was employed to obtain the linearized form of the nonlinear equations of motion. Either the asymmetry of rotor or rub-impact can result in instability and make the problem difficult to solve. Thus, the arc-length method was utilized to trace the branch of the solutions. In order to improve the calculation speed and accurately predict the solution, the alternating frequency/time domain (AFT) was adopted to calculate the iteration of the arc-length method. Based on the proposed method, the effects of stator stiffness, gap size, unbalance, and asymmetric in shaft on the steady-state response and stability were obtained.
Asymmetric rotor systems widely exist in commercial plants. In the previous studies about asymmetric rotor systems, parameters such as material properties and boundary conditions are deterministic. To obtain a deep understanding of the dynamics of asymmetric rotor systems, a generator rotor system considering uncertain factors is studied in this paper. The equations of motion of the three-dimensional finite element model are solved in the rotating frame. The component mode synthesis is used to reduce the degrees of freedom. By employing the Chebyshev interval method (CIM), the uncertain gravity responses of the generator rotor system are investigated. The influences of the uncertainties in the bearing's properties and the rotor's material properties on the gravity response are studied in cases with a single uncertainty and double uncertainties. The accuracy and the efficiency of CIM are validated by comparing with the results of the scanning method. The results show that uncertainties have remarkable influences on the gravity response, and that these influences are different from each other. The proposed method and the results can provide guidance to the design and optimization of the rotary machinery. Appl. Sci. 2019, 9, 3036 2 of 15 the modeling techniques based on beam elements were gradually replaced by a three-dimensional finite element model (3D FEM). Rao and Sreenivas [10] modeled the asymmetric rotor by using 3D finite elements. The transient response due to unbalance alone and gravity alone were investigated. The gravity critical speed was reported in their study. Lazarus et al. [11] established the 3D FEM of the rotary part and stationary part in the rotating frame and fixed frame, respectively. The global equations of motion were obtained by coupling the two parts in a different frame. To accelerate the stability and steady-state analysis, component mode synthesis (CMS) was used to reduce the degrees of freedom (DOFs). Wang et al.[12] used a free-interface CMS to establish a reduced-order model (ROM). Thus, the DOFs of anisotropic rotor-bearing systems were reduced. The influences of four dimensionless parameters describing the anisotropy of bearing on the unbalance and gravity responses were analyzed and discussed. Ma et al. [13] experimentally and numerically studied the whirl speed of an asymmetric rotor system. In their numerical analysis, 3D FEM combined with model order reduction using modal shapes was employed. Then, their model order reduction technique was employed by Zuo et al. [14] to study the instability of the asymmetric rotor system with uncertainties. Zheng et al. [15] proposed a method that can reduce the interface DOFs when multiple substructures were used. This method was able to solve the steady-state response of large-scale asymmetric rotor systems.The above studies indicated that valuable results concerning the stability and steady-state response of asymmetric rotors have been obtained by deterministic study, where the properties of rotor system and boundary conditions were de...
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