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OPTIMAL CONTROL CONFIGURATION OF HEATING AND HUMIDIFICATION PROCESSES part I

Liliana Teodoros, Bjarne Andresen

2011
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U.P.B. Sci. Bull., Series D
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unpublished

In prezenta lucrare se iau in considerare procesele fundamentale de transfer de caldura si control al umiditatii iar procesul politropic de incalzire a aerului cu modificarea umiditatii este analizat prin prisma teoriei optimizarii. Scopul este de a gasi metode optime de a incalzi si umidifica aerul producind entropie minima. Am considerat interactiunea in contra-curent dintre aer exterior rece si apa calda aduse in contact intr-un echipament special destinat umidificarii. Acest studiu se
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... a pe teoria controlului optimal iar scopul sau este gasirea parametrilor optimi pe baza generarii minime de entropie asociate procesului.Folosim teoria optimizarii pentru a analiza modul in care prin varierea suprafatei de contact dintre aer si apa se obtin temperatura si umiditatea dorite pentru aer la iesirea din echipamentul de umidificare.Temperatura apei si cantitatea de apa optime la intrarea in umidificator sint determinate. The fundamental heat transfer and humidity control processes are considered and the polytropic process of heating air while modifying the humidity contents is analyzed using the optimal control theory. The aim is to investigate optimal ways of heating and humidifying the air while producing minimum entropy. Heating and humidification are considered here in a counter current interaction between dry, cold outdoor air and hot water in a device purposely used for bringing air in contact with water. This study is based on the theory of optimal control and its aim is to find the optimal parameters based on the minimum entropy production associated to the process. We use optimal control theory to analyze how varying the contact surface between water and air achieves the desired temperature and humidity of the air at the exit of the humidifying device. The optimal water temperature and amount at the inlet are also determined. Nomenclature Latin symbols A = area of water surface in contact with air; B = atmospheric pressure C 1 ... C 5 = empirical coefficients; C v = heat capacity d = number of controls; d = vector of controls for the process F = vector of evolution expressions for n G(n 1 , t 1) = desired combination of state functions at the final time 4 Liliana Teodoros, Bjarne Andresen G = vaporization rate of water; H = Hamiltonian of optimization ∆H = enthalpy of water vapor; I = cost (object) functional for the process k = coefficient of heat transfer; L = rate of dissipation M = molar mass; m v = mass of water vapor per volume of air m w = mass of water in the water layer per area of surface of water-air contact n = number of state functions; n = vector of state functions of the system p = partial pressure of water; Q = rate of heat transfer R = ideal gas constant ΔS = entropy change (production) during the process T = temperature; t = time; v = air velocity over water surface V = volume; x = position in flow direction y = width of channel; z = height of air channel Superscripts * = optimal value s = ds/dt Subscripts 0 = initial value; 1 = final value; a = related to air sat = at saturation; v = related to vapor; w = related to water Greek symbols λ = latent heat of water; ψ = vector of co-state (adjoint) variables ω = vector of state variables T a , T w , m v , m w ; φ = relative humidity of air

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