Stability Analysis and Optimization of By-Pass Controlled Heat Exchanger With Boiling

1976 ◽  
Vol 98 (2) ◽  
pp. 161-166 ◽  
Author(s):  
J. S. Ansari
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Stability Analysis ◽  
Heat Exchanger ◽  
Flow Rate ◽  
Distributed Parameter ◽  
Final Temperature ◽  
Razumikhin Theorem ◽  
Sustained Oscillations ◽  
Intermediate Variables

A heat exchanger with boiling is considered. The final temperature of steam is controlled with the help of a controller which regulates the flow rate of by-pass water mixing with the outcoming steam. The simplest known mathematical model retaining the nonlinear and distributed parameter nature of the process is adopted. A known method of analysis, namely, Liapunov-Razumikhin theorem, is used to derive results on stability. An interesting feature of the system is that a positive feedback is required for stability. If the control is designed on the basis of minimization of the error in the final temperature alone, then the optimal control, requiring a negative feeedback, leads to sustained oscillations in the intermediate variables, even when the output is steady. The analysis, therefore suggests that meaningful optimization must take into account fluctuations in intermediate variables in addition to the error. A derivative control is shown to improve the transient response.

Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy

2019 ◽  
Vol 20 (3-4) ◽  
pp. 269-285 ◽  
Author(s):  
Subhas Khajanchi
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Stability Analysis ◽  
Model Simulation ◽  
Equilibrium Points ◽  
Glioma Cells ◽  
Adjoint System ◽  
Cellular Immunotherapy ◽  
Theory Of Optimal Control ◽  
Malignant Glioma Cells

AbstractWe investigate a mathematical model using a system of coupled ordinary differential equations, which describes the interplay of malignant glioma cells, macrophages, glioma specific CD8+T cells and the immunotherapeutic drug Adoptive Cellular Immunotherapy (ACI). To better understand under what circumstances the glioma cells can be eliminated, we employ the theory of optimal control. We investigate the dynamics of the system by observing biologically feasible equilibrium points and their stability analysis before administration of the external therapy ACI. We solve an optimal control problem with an objective functional which minimizes the glioma cell burden as well as the side effects of the treatment. We characterize our optimal control in terms of the solutions to the optimality system, in which the state system coupled with the adjoint system. Our model simulation demonstrates that the strength of treatment $u_{1}(t)$ plays an important role to eliminate the glioma cells. Finally, we derive an optimal treatment strategy and then solve it numerically.

Modelling and Dynamics Analysis of Heat Exchanger as a Distributed Parameter Process

2004 ◽  
Author(s):  
B. Savic ◽  
D. Lj. Debeljkovic
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Heat Exchanger ◽  
Fuel Oil ◽  
Distributed Parameter ◽  
Dynamics Analysis ◽  
Real Process ◽  
Cooling Chamber ◽  
Constant Coefficients ◽  
Process Behavior

On the basis accepted and critically clarified assumptions, a non–linear and afterwards linearized mathematical model of fuel oil cooling chamber has been developed in engineering sense sufficiently correct. The model is in the form of set of partial differential equations with constant coefficients. Using the appropriate numerical simulation of the results derived, the dynamic of this process has been shown in the form of appropriate transient processes responses which quite well correspond to the real process behavior.

Interaction Between Secondaries in a Thermal-Hydraulic Network

2006 ◽  
Vol 128 (4) ◽  
pp. 820-828 ◽  
Author(s):  
Weihua Cai ◽  
Walfre Franco ◽  
Gregor Arimany ◽  
Mihir Sen ◽  
K. T. Yang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Heat Exchanger ◽  
Flow Rate ◽  
Significant Interaction ◽  
Step Change ◽  
The Other ◽  
Thermal Interaction ◽  
Order Of Magnitude ◽  
Hydraulic Network

The design of one secondary loop of a complex network often neglects the effect that its operation has on the others. The present is a study of hydrodynamic and thermal interaction between secondaries in a thermal-hydraulic network as the system goes from one steady state to another. Experimental results are related to those derived from a mathematical model. The network consists of a primary and three secondary loops. There is a water-to-water heat exchanger on each secondary, with the cooling coming from the primary and the heating from a separate loop. A step change is introduced by manually actuating a valve in one of the secondaries, resulting in changes in the other loops also. The response time of the temperature is found to be an order of magnitude higher than that of the flow rate, which is again an order of magnitude higher than the pressure difference. The steady-state results show that there is significant interaction, and that it is dependent on the initial operating condition. The hydrodynamic and thermal responses are found to be very different.

scholarly journals Energy analysis of heat exchanger in a heat exchanger network

2018 ◽  
Vol 22 (5) ◽  
pp. 1999-2011 ◽  
Author(s):  
Martina Rauch ◽  
Antun Galovic
Keyword(s):  
Mathematical Model ◽  
Heat Exchanger ◽  
Heat Flow ◽  
Flow Rate ◽  
Local Extremum ◽  
Heat Flow Rate ◽  
Fluid Stream ◽  
Heat Exchanger Network ◽  
Maximum Heat ◽  
The Given

For many years now, heat exchanger optimization has been a field of research for a lot of scientists. Aims of optimization are different, having in mind heat exchanger networks with different temperatures of certain streams. In this paper mathematical model in dimensionless form is developed, describing operation of one heat exchanger in a heat exchanger network, with given overall area, based on the maximum heat-flow rate criterion. Under the presumption of heat exchanger being a part of the heat exchanger network, solution for the given task is resting in a possibility of connecting an additional fluid stream with certain temperature on a certain point of observed heat exchanger area. The connection point of additional fluid stream determines the exchanging areas of both heat exchangers and it needs to allow the maximum exchanged heat-flow rate. This needed heat-flow rate achieves higher value than the heat-flow rate acquired by either of streams. In other words, a criterion for the existence of the maximum heat-flow rate, as a local extremum, is obtained within this mathematical model. Results of the research are presented by the adequate diagrams and are interpreted, with emphasis on the cases which fulfill and those which do not fulfill the given condition for achieving the maximum heat-flow rate.

scholarly journals Stability Analysis of a Flow-Rate Controlled Heat Exchanger

1975 ◽  
Vol 11 (2) ◽  
pp. 239-244 ◽  
Author(s):  
Shinzo KITAMURA ◽  
Hideaki KANOH ◽  
Mitsuyoshi KOJYO ◽  
Shotaro NISHIMURA
Keyword(s):  
Stability Analysis ◽  
Heat Exchanger ◽  
Flow Rate ◽  
Rate Controlled

A Soft-Sensing Technique for Measurement of Mass Flow Rate in a Liquid-Liquid Heat Exchanger

2015 ◽  
Author(s):  
Sangeeta Nundy ◽  
Siddhartha Mukhopadhyay ◽  
Alok Kanti Deb
Keyword(s):  
Heat Exchanger ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Temperature Measurements ◽  
Distributed Parameter ◽  
Outlet Temperature ◽  
Soft Sensing ◽  
Distributed Parameter Model ◽  
Liquid Heat

This paper presents a soft-sensing technique of determining the mass flow rate of a liquid-liquid heat exchanger using temperature measurements and a distributed parameter model. The efficiency of a heat exchanger is intimately related to its mass flow rate and as a consequence mass flow rate measurements are essential for any fault detection or monitoring program of the heat exchanger. However the costly mass flow rate sensor measurements can be bypassed by this soft-sensing technique which primarily employs measurements from inexpensive temperature sensors. We first develop a distributed parameter model of the counter flow type heat exchanger using energy balance equations. Thereafter, a state-space model of the heat exchanger is formulated using orthogonal collocation method where temperature at the collocation points and the unknown mass flow rate are considered as the state variables. The mass flow rate is estimated by a Hybrid Extended Kalman Filter algorithm using the outlet temperature measurements. The sensitivity of the soft-sensing technique in presence of modeling errors and measurement noise is also studied using a suitable simulation example.

scholarly journals MODELING OF Q-H CHARACTERISTICS OF THE ELECTRIC DRIVE WITH A VORTEX ELECTRICAL PUMP

2015 ◽  
pp. 133-137
Author(s):  
A. M. Sagdatullin
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
General Expression ◽  
Flow Rate ◽  
Electric Drive ◽  
Control Limit ◽  
Electric Pump ◽  
Vortex Pump ◽  
Working Section ◽  
Range Of Values

In this paper we consider the possibility of modeling the performance characteristics of the electric drive with a vortex electric pump. The structure of the vortex electric pump studied for the experiment is considered, as well as its Q-H characteristic. To determine the optimal control limit of square-law characteristic of H = f (Q) we offer an ade-quate mathematical model of working Q-H characteristics of the electric vortex pump Pk 200. It is concluded that for studying and searching for optimal performances of the vortex pump Pk 200 the model of square-law characteristic H = f (Q) in accordance with the general expression for the working section can be applied within a certain range of values, i.e. the flow rate from Q1 (1,5) to Q2 (3,5) and the pressure from H1 (67) to H2 (30).

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