SB,
Without getting too far into the theory of an expansion compressor and turbine, perhaps it's best to simplify what's occuring in order to make it easier to understand.
The purpose of the air conditioning pack is to make bleed air safe and acceptable for use pressurizing the cabin...make it safe and tolerable for the cabin occupants. As we discussed before, the bleed air is hot, so the primary function of the pack is to cool the air. What the pack is doing is extracting heat energy.
To do this, initially, a heat exchanger is used. This is the same as a radiator on a car, practically speaking. In a car, hot water is circulated through a radiator, and cooler air blows through the radiator. Heat is exchanged from the hot water, to the air. As a result, the air leaving the radiator is warmer, or hotter than the air entering the radiator, because as it passes through the radiator, heat is transferred or exchanged from the water to the air.
In the airplane, a bleed air heat exchanger does the same thing, except that the radiator doesn't have water passing through it, it's got hot bleed air. Cooler external air from outside the airplane passes through the radiator, and the heat energy from the bleed air is transferred to the external ram air this way in the heat exchanger. The pictures you posted showing the underside of a Boeing 747, show three pack inlet openings which permit ram air from outside the aircraft to flow through heat exchangers for each respective air conditioning pack in the airplane.
You'll also see some square shapes to the rear, or bottom of the picture...these are the pack outlets. Air goes in the areas you circled, goes through the heat exchangers to extract heat from the bleed air in the packs, and then passes out the pack outlet doors.
Think about this heat extraction process a little like extracting water from a wash cloth. Prior to putting the air through the heat exchanger, the air is "squeezed" by compressing it. It's this compressed air that is run through the heat exchanger. By compressing the air, the temperature is raised even more, providing more energy that can be extracted. This is a little like wringing or twisting a rag to get all the water out of it. The bleed air is compressed and then the energy extracted in order to get as much as possible out of it during the heat exchange process.
In fact, the ACM uses a water extractor too, because while it's extracting heat, it's also extracting moisture, and it removes water to prevent the ACM from freezing up. AMC's are so effective that I've seen some aircraft blow snow out of the air conditioning vents during operations in high humidity, and we regularly see thick fog or mist in the airplane under certain conditions on the ground.
In order to control the amount of cooling or extraction that takes place in the heat exchanger, the door position can be varied. Also in order to control the heating and cooling that takes place in the pack, a turbine bypass valve is used which allows bleed air to go through the heat exchanger, then go around the expansion turbine, instead of going through it.
Just like the compressor was used to compress air and heat it up, an expansion turbine is used after the heat exchanger in order to drop air pressure and cool the air even more. Compress air, it heats up, allow it to expand, it cools down, and it's the cooler air that's desired. This is the same process that takes place in any air conditioning system. The big difference between what's going on here, and what goes on in your car is that the car uses an enclosed system with refrigerant that undergoes the same process and the bleed air is undergoing here, and in your car this refrigerant then extracts heat energy from the air that blows on you. In the airplane, the liquid refrigerant is skipped, and the bleed air is run through the same process to condition the air for your use.
You asked about the compressor in the pack air cycle machine. The compressor isn't there to boost pressure for use. We get our air pressure from the engines...it's pressurized by the engine compressors. What's referred to as the compressor in the pack ACM is a device that is used to briefly compress the air in order to extract heat energy, that's all. The bleed air arrives with all the pressure that's required to fulfill it's various functions, such as operate flight controls (leading edge devices, for example), or pressurize the cabin. The pack doesn't boost this pressure; it simply conditions the temperature for cabin use.
Is it really necesary to maintain inside temperature with an open loop system - energy transsfer between inside and outside of a fuselage isn't done through the heat exchangers but rather directly - warm or cold air is constantly flowing throug fuselage.
It's not necessary to maintain temperature with an open loop system. It's necessary to maintain pressure. We have a continuous supply of bleed air, and this bleed air is too hot to use directly in the cabin. To make it safe for use, we must condition it, and conditioning the air by regulating it's temperature is a key part of pressurizing the cabin. Pressurizing is necessary for comfort, safety, and life support.
Energy transfer IS done by the heat exchangers. In the packs.
But one is for certain, any heat taken from the engine is a loss of energy, so why cargo planes, that don't even need lots of air refreshing don't have this kind of system where bleed air is warming the fuselage via heat exchanger?
Cargo aircraft have the same need for pressurization that any other aircraft requires. Additionally, regulating the temperature in cargo compartments is also important. Our cargo aircraft have carried everything from military equipment to full sized whales to teams of race horses to perishible flowers. Maintaining internal temperatures is important for cargo, personnel inside the airplane (we breathe the same air that passes around the cargo), and it's important for proper operation of aircraft systems.
Bleed air must be cooled, in order to warm the fuselage, else it warms the fuselage too much. Heat exchangers aren't used to warm the fuselage. They're used to cool the air that pressurizes the fuselage.
I get the impression that you think an air cycle machine is unnecessary complexity, but the truth is it's utter simplicity. It requires less energy, and fewer steps, to condition the air than any other type of air conditioning system except perhaps an evaporative cooler.
Could instead of air to air heat exchangers, cooling of bleed air will be done by liquid to air heat exchanger with fuel as liquid.
Of course they could, and some aircraft air conditioning systems use freon or other refrigerant, just like your car. However, for large aircraft, the extra weight and complexity, the need for additional electrical compresors, etc, negate any such value. An ACM is more simple, more reliable, easier to maintain, and can handle the volume of air required for a large cabin much better than a liquid refrigerant air conditioning system. More importantly, it's necessary in order to make the air useable to pressurize the cabin.
Smaller airframes can get away with simply mixing cold ram air with bleed air through flow control systems, to come up with an acceptable cabin temperature. This doesn't work so well in a big airframe with large volumes of airflow. It's much more simple to simply condition the air being used to pressurize the aircraft, and then fine tune it with some warm trim air.
As I know jet fuel is certified for operating down to -37°C. 30-36,000 feet above is -56°C so is fuel really heated just prior it is injected into the combustion chamber?
Various systems are used to warm fuel. Fuel-oil heat exchangers are common. These exchange heat between aircraft fuel sources and engine oil. We use fuel to cool hydraulic fluid, too. We heat fuel at certain times when it's about to enter the fuel control unit on the engine, using bleed air. However, this must be monitored very closely and can't be a continuous process. We have schedules spelled out regarding how frequent and how long we can apply fuel heat.
Numerous types of fuel and fuel formulations exist; not all of them have freezing points at -37 deg C. This represents a range for cut fuels (fuels containing gasoline products as well as kerosine). Fuels such as Jet A have freezing points which are lower, around -54 degrees C.
There are other ways to warm fuel. Transferring fuel can warm it. The quantity of fuel affects temperature; bigger tanks with more quantity and capacity maintain temperature better than smaller, thinner tanks with lower capacity and quantity. A bette system has to be found to cool bleed air for cabin use, however, than running it all the time through fuel, because there are many times when heating the fuel isn't desirable. Accordingly, using air cycle machines with heat exchangers and expansion turbines works very well, and very reliably...the reason they're so widespread in their use. they're light weight, simple, and consistent.
If the bleed air will be cooled down trough wing's leading edges, (doing usefull job) and fuel, the energy taken away from engine will be renewed throug fuel that is sooner or later injected to the engine. Aslo at plane stationary on the ground with hot outside temperatures, bleed air could be cooled down to temp od a fuel and when decompressed throug expansion turbine it will be cool enough to make its job.
I have no idea what you just said.