1-D stady state conduction High-temperature reusable ...
4
1-D stady state conduction High-temperature reusable surface insulation (HRSI) The HRSI comprises three layers that protect the structure in aluminum as shown in the figure. The first layer is in RCG (reaction cured glass) whose temperature at radiative equilibrium is 1530 K, the second layer is a silica insulation and the third layer is a strain isolator pad (SIP) (whose maximum allowable temperature is 700 K). The structural layer is a plate of 0.813 mm thickness of aluminum. Assume the layers to be in very good thermal contact. T 0 = 1530 K (1260 °C) T MAX_SIP = T 1_MAX = 700 K T MAX_ALU = T 2_MAX = 450 K T 3 = 298.15 K t ALU = 0.813 mm t RCG = 0.38 mm q = 183 kW/m 2 (95% of which is re-radiated) Figure. Layers in HRSI. The first layer has mechanical characteristics to resist to the dynamic pressure and impacts. A coating to maximize the radiative cooling is applied on it. We can assume the first layer at the same temperature because the high thermal conductivity and the little thikness (0.38 mm) of this layer. The temperature T 0 on the RCG is then 1530 K while the temperature T 2 on the aluminum plate has to be less then 450 K. The heat loss through the thermal protection is expected to be the 5% of the incoming flux 183 kW/m 2 (the 95% is reradiated to the environment by the coating) Determine the thickness of SiO 2 and SIP that results in the minimum total thickness of the TPS. Given thermal conductivities and thermal expansion coefficients in: Layer k W/(m K) α (1E-06/K) SiO 2 1.4 0.4 SIP 0.033 Aluminum 247 23.6
Transcript of 1-D stady state conduction High-temperature reusable ...
1-D stady state conductionHigh-temperature reusable surface insulation (HRSI)
The HRSI comprises three layers that protect the structure in aluminum as shown in the figure. The first layer is in RCG (reaction cured glass) whose temperature at radiative equilibrium is 1530 K, the second layer is a silica insulation and the third layer is a strain isolator pad (SIP) (whose maximum allowable temperature is 700 K). The structural layer is a plate of 0.813 mm thickness of aluminum. Assume the layers to be in very good thermal contact.
T0 = 1530 K (1260 °C)
TMAX_SIP = T1_MAX = 700 K
TMAX_ALU = T2_MAX = 450 K
T3 = 298.15 K
tALU = 0.813 mm
tRCG = 0.38 mm
q = 183 kW/m2 (95% of which is re-radiated)
Figure. Layers in HRSI.
The first layer has mechanical characteristics to resist to the dynamic pressure and impacts. A coating to maximize the radiative cooling is applied on it. We can assume the first layer at the same temperature because the high thermal conductivity and the little thikness (0.38 mm) of this layer. The temperature T0 on the RCG is then 1530 K while the temperature T2 on the aluminum plate has to be less then 450 K. The heat loss through the thermal protection is expected to be the 5% of the incoming flux 183 kW/m2 (the 95% is reradiated to the environment by the coating) Determine the thickness of SiO2 and SIP that results in the minimum total thickness of the TPS.
Given thermal conductivities and thermal expansion coefficients in:
Layer k W/(m K)
α (1E-06/K)
SiO2 1.4 0.4 SIP 0.033
Aluminum 247 23.6
Conduzione del calore staz. 1-D con condizioni al contorno convettive
Si consideri una finestra vetrata delle dimensioni 0,8mx1,5m e dello spessore di 8 mm, caratterizzata da una conducibilità termica λ = 0,78 [W/(m°C)]. Si determinino la potenza termica stazionaria trasmessa attraverso la finestra e la superficie interna della finestra in un giorno in cui l’ambiente interno è a temperatura Ti = 20°C e l’ambiente esterno è a temperatura Te = -10°C. Si assumano quali coefficienti di scambio termico sulle superfici esterna ed interna della finestra he = 40[W/(m2°C)] e hi = 10[W/(m2°C)], includendo in essi gli effetti dell’irraggiamento termico.
Dati λ = 0,78 [W/(m°C)] hi = 10[W/(m2°C)] he = 40[W/(m2°C)] Area vetrata Av =1,2 [m2]Te = -10°CTi = 20°Cs = 8 [mm]
s
Rifare l’esercizio precedente, ipotizzando che la finestra vetrata alta 0,8 (m) e larga 1,5 (m) sia costituita da due strati di vetro di spessore di 4 mm [λ = 0,78 W/(m°C)], separati da un’intercapedine d’aria ferma spessa 10 mm [λ = 0,026 W/(m°C)]. Si determinino allora la potenza termica stazionaria trasmessa attraverso la finestra e la superficie interna della finestra in un giorno in cui l’ambiente interno è a temperatura Ti = 20°C e l’ambiente esterno è a temperatura Te = - 10°C. Si assumano quali coefficienti di scambio termico sulle superfici esterna ed interna della finestra he = 40[W/(m2°C)] e hi = 10[W/(m2°C)], includendo in essi gli effetti dell’irraggiamento termico.
Te = -10°C
Ti = 20°C
Conduzione del calore transitoria 1-D
Si consideri una parete infinita dello spessore di 20 mm, caratterizzata da una conducibilità termica λ = 0,78 [W/(m°C)], un calore specifico cp = 7500 [J/(kg °C)] e densità ρ = 2180 [kg/m3]. La superficie in x = 0 sia ad una temperatura imposta Ta = 40°C mentre la superficie in x = L sia ad una temperatura imposta Tb = 0 °C. All’istante iniziale è presente una distribuzione di temperatura:
TINIT = TMAX sin ( π x / L ), in cui TMAX = 40 °C.
Si valuti l’evoluzione della distribuzione di temperatura lungo x in un intervallo di tempo di 1000 secondi. Si ripeta l’analisi considerando delle condizioni al contorno adiabatiche.
