Zdravko Virag

Truncated method of characteristics for quasi-two-dimensional water hammer model

AbstractA new and efficient variant of the method of characteristics for solving the quasi-two-dimensional water hammer model is proposed. The method requires the fully implicit discretization scheme for radial velocity, to eliminate this velocity from the equations for axial velocity and piezometric head. As the radial velocity is typically outside the scope of interest, the computation time is reduced by omitting its calculation. The proposed method is compared with an existing method by means of two water hammer benchmark tests. The results of the two methods practically match, but the proposed method requires approximately 50% less CPU time for the laminar flow test, and 30% for the turbulent one. In addition, the numerical accuracy of four implicit interpolation schemes is compared for the case of laminar flow. The obtained results suggest that the required fully implicit discretization is not a significant limitation of the proposed method. The new method offers high numerical efficiency, while reta...

Analytical Entropy Analysis of Recuperative Heat Exchangers

The analytical solutions for the temperature variation of two streams in parallel flow, counter flow and cross-flow heat exchangers and related entropy generation due to heat exchange between the streams are presented. The analysis of limiting cases for the relative entropy generation is performed, and corresponding analytical expressions are given. The obtained results may be included in a more general procedure concerning optimal heat exchanger design.

Efficient solution method for quasi two-dimensional model of water hammer

ABSTRACT An existing solution method for the quasi two-dimensional model of transient flow in pipes has already been recognized as accurate, robust, and consistent with the physics. Its main disadvantage – numerical inefficiency, has recently been considerably reduced by introducing an improved solution procedure. This paper proposes a new and even more efficient solution procedure. The proposed method gives results that match the results of existing methods, but requires approximately 10% less central processing unit time than the improved procedure.

Noninvasive determination of the pulmonary artery input impedance

A reliable noninvasive method for the estimation of pulmonary function in healthy and diseased subjects should be of great importance in the prognosis, diagnosis, and treatment of pulmonary hypertension. Here we propose such a method, which is based on the parameter identification of the five-element Windkessel model of pulmonary circulation. The method requires the following input variables: the heart rate, the stroke volume, the Doppler echocardiographic measurements of the tricuspid regurgitation and the pulmonary valve velocity profiles, and estimations of the right atrium and the pulmonary vein pressure. The stroke volume is calculated as a product of the left ventricle outflow tract area and the velocity-time integral measured at the same place. The model parameter identification procedure is based on minimization of the root mean square error between the pulmonary artery root pressure calculated from the aforementioned Doppler velocity profiles (from the Bernoulli equation applied during the ejection phase) and the pressure from the Windkessel model during the same period. The output from the model contains the calculated pulmonary artery input impedance (i.e. the model parameters: pulmonary vascular resistance, pulmonary artery proximal and distal compliances, inertance, and characteristic impedance) and the pulmonary artery pressure profile during the whole heart period. Our method is applied to a subject with pulmonary hypertension. The right heart Swan-Ganz catheterization has been performed in this subject. The results obtained by using this method show that the five-element Windkessel model reconstructs the main features of the pulmonary artery input impedance very well: its modulus shows the minimum where the phase angle changes its sign. The pulmonary vascular resistance, the systolic, diastolic and mean pulmonary artery pressures obtained from the method are in good agreement with the values obtained invasively from the catheterization. Sensitivity analysis shows that the mean pulmonary pressure is fairly insensitive to slight overestimation/ underestimation of all input parameters, except for the right atrium pressure. The absolute error in the mean pulmonary artery pressure is nearly the same as the error in the right atrium pressure. Since the proposed method offers a deeper insight into the pulmonary circulation than the catheterization itself because it provides the proximal and distal compliance, the inertance and the characteristic impedance, it seems that it can serve in clinical practice as a good substitute for catheterization.

Another view on the optimization of the Brayton cycle with recuperator

Nondimensional expressions for the work output, thermal efficiency, heat input, and entropy generation number in the Brayton cycle with a recuperator are given as functions of seven input parameters: pressure ratio, temperature ratio, recuperator effectiveness, turbine and compressor isentropic efficiencies, nondimensional pressure drop in the combustor and recuperator and the ratio of specific heat capacities. The expressions for pressure ratios which maximize or minimize the considered quantities are derived. Since it is not possible to maximize all the quantities at a unique value of pressure ratio, three optimization criteria: (i) maximum work output, (ii) maximum thermal efficiency, and (iii) maximum of their weighted sum are defined. For each criterion two diagrams from which one can select optimal pressure ratio and read out all basic quantities defining the Brayton cycle are provided. In the case of criterion of maximum thermal efficiency, when the recuperator effectiveness is lower than the certain limit, the Brayton cycle without a recuperator is better than that with it. In the case of other two criteria, the Brayton cycle with a recuperator is always better than that without it, regardless of the value of the recuperator effectiveness.

A fast method for solving a linear model of one-dimensional blood flow in a viscoelastic arterial tree

For the purpose of optimization of the whole arterial tree, a fast method for solving of one-dimensional model of blood flow is required. A semi-analytic transmission line method for solving a linearized one-dimensional model of blood flow in an arterial tree with viscoelastic walls is proposed. The transmission line method that solves the linearized model in the frequency domain and the method of characteristics that solves either linearized or non-linear one-dimensional models in the time domain are compared regarding accuracy and computational time. For this purpose, the benchmark problem of a 37-artery network with available experimental data is used. In the case of the linearized model, the results from the transmission line method and the method of characteristics are practically the same. The difference between the transmission line method solution of the linearized model and the method of characteristics solution of the non-linear model is much smaller than the error of either method of characteristics or transmission line method numerical solutions with respect to the experimental data. For typical applications, the transmission line method is at least two orders of magnitude faster than the method of characteristics.