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Short answer

This space is part of the inter-turbine duct (ITD), it is required, as well as the larger LPT stage 1 vanes, to maintain a satisfactory aerodynamic flow between HPT and LPT rotating at different speeds (in the ratio of 1:3) and having different diameters.

Shortened ITD are complex to design and known under the name of aggressive ITD.

Details

Taking the CFM56-7B (Boeing 737 NG) as an example. This engine has a single stage HPT and a 4 stage LPT.

Each rotor is preceded by stator (nozzle). The role of the stator vanes is to convert pressure into velocity and turn the flow more perpendicular to the rotor blades surface (this is opposite to the compressor stages where the vanes are downstream of the blades to convert added velocity into pressure and straighten the flow).

There is a larger space ahead of the LPT stage 1 vanes.

Small gap and larger vanes

Everything is globally continuous, though there is a small gap forward of the LPT stage 1 nozzle which is located in the HPT casing. The vanes themselves are larger axially.

^{CFM56-7B, small gap before LPT Stage 1 vanes}

This location is called the inter-turbine (transition) duct, it corresponds to the interface between HPT and LPT which are rotating at different speeds. The duct has an increasing area due to its "S" shape.

^{Inter-turbine duct geometry. Source}

The gap allows to get a smother change and the adequate duct aspect ratio. The longer duct prevents significant pressure loss before reaching the LPT.

To increase engine performance, manufacturers are trying to decrease the length of the duct but this is difficult due to aerodynamic reasons. Shorter ducts are known as aggressive inter-turbine ducts (AITD). See this paper. A similar duct exists between LPC and HPC.

Bearings

Regarding the possible problem with a bearing or a bearing support in the way, the bearings are really smaller than the stages:

^{CFM56-7B, location of rear bearings}

• The No 4 bearing is within the HP shaft.
• The No 5 outer support is within the oil collector shown above, and the bearing itself is within the its support.

Short answer

This space is part of the inter-turbine duct (ITD), a duct which is required to maintain a satisfactory flow continuity between HPT and LPT rotating at different speeds (in the ratio of 1:3) and having different diameters. The duct is made of the gap and the larger (in the axis direction) LPT stage 1 vanes.

Note this duct is a diffuser as the annular area is growing along the flow path. What happens in this diffuser is not very well known and its design has been empirical to some extend, using guides like this:

^{Pressure recovery vs friction. Source}

Some numerical simulation demonstrated the design indeed influences the LPT (pressure loss in the duct), but also the HPT and the combustion. On days where saving 1% fuel (therefore 1% CO2) is important, some effort is now done on the optimization of the inter-turbine duct.

Shortened ITD are complex to design and known under the name of aggressive ITD.

Details

Taking the CFM56-7B (Boeing 737 NG) as an example. This engine has a single stage HPT and a 4 stage LPT.

Each rotor is preceded by stator (nozzle). The role of the stator vanes is to convert pressure into velocity and turn the flow more perpendicular to the rotor blades surface. This is opposite to the compressor stages where the vanes are downstream of the blades to convert velocity added by the blades into pressure, maintain velocity constant and straighten the flow.

Gap and larger vanes

Everything is globally continuous, though there is a a gap forward of the LPT stage 1 nozzle located in the HPT casing. The vanes themselves are larger axially.

^{CFM56-7B, small gap before LPT Stage 1 vanes}

This location is called the inter-turbine (transition) duct, it corresponds to the interface between HPT and LPT which are rotating at different speeds. 

The duct has an increasing area due to the larger diameter and size of the LPT stage 1 rotor (a similar duct exists between LPC and HPC for the same reasons).

^{Inter-turbine duct geometry. Source}

The gap is chosen to set (empirically) the adequate duct slope, aspect ratio, etc for an acceptable pressure loss between the turbines.

To increase engine performance, manufacturers are trying to decrease the length of the duct but there is a lack of knowledge in this domain. 

Shorter ducts are known as aggressive inter-turbine ducts (AITD). See this paper.

Bearings

Regarding the reason mentioned in another answer, a possible problem with a bearing or a bearing support in the way: This is not actual, the bearings are much smaller than the turbine stages:

^{CFM56-7B, location of rear bearings}

• The No 4 bearing is between the HPT shaft and the LPT shaft.
• The No 5 outer support is within the oil collector, and the bearing itself is within the its support.

Short answer

This space is part of the inter-turbine duct (ITD), it is required, as well as the larger LPT stage 1 vanes, to maintain a satisfactory aerodynamic flow between HPT and LPT rotating at different speeds (in the ratio of 1:3) and having different diameters.

Shortened ITD are complex to design and known under the name of aggressive ITD.

Details

Taking the CFM56-7B (Boeing 737 NG) as an example. This engine has a single stage HPT and a 4 stage LPT.

Each rotor is preceded by stator (nozzle). The role of the stator vanes is to convert pressure into velocity and turn the flow more perpendicular to the rotor blades surface (this is opposite to the compressor stages where the vanes are downstream of the blades to convert added velocity into pressure and straighten the flow).

There is a larger space ahead of the LPT stage 1 vanes.

Small gap and larger vanes

Everything is globally continuous, though there is a small gap forward of the LPT stage 1 nozzle which is located in the HPT casing. The vanes themselves are larger axially.

^{CFM56-7B, small gap before LPT Stage 1 vanes}

This location is called the inter-turbine (transition) duct, it corresponds to the interface between HPT and LPT which are rotating at different speeds. The duct has an increasing area due to its "S" shape.

^{Inter-turbine duct geometry. Source}

The gap allows to get a smother change and the adequate duct aspect ratio. The longer duct prevents significant pressure loss before reaching the LPT.

To increase engine performance, [manufacturers are trying to decrease the length of the duct][4] but this is difficult due to aerodynamic reasons. Shorter ducts are known as aggressive inter-turbine ducts (AITD). See [this paper][5]. A similar duct exists between LPC and HPC.

Bearings

Regarding the possible problem with a bearing or a bearing support in the way, the bearings are really smaller than the stages:

^{CFM56-7B, location of rear bearings}

• The No 4 bearing is within the HP shaft.
• The No 5 outer support is within the oil collector shown above, and the bearing itself is within the its support.

Short answer

This space is part of the inter-turbine duct (ITD), it is required, as well as the larger LPT stage 1 vanes, to maintain a satisfactory aerodynamic flow between HPT and LPT rotating at different speeds (in the ratio of 1:3) and having different diameters.

Shortened ITD are complex to design and known under the name of aggressive ITD.

Details

Taking the CFM56-7B (Boeing 737 NG) as an example. This engine has a single stage HPT and a 4 stage LPT.

Each rotor is preceded by stator (nozzle). The role of the stator vanes is to convert pressure into velocity and turn the flow more perpendicular to the rotor blades surface (this is opposite to the compressor stages where the vanes are downstream of the blades to convert added velocity into pressure and straighten the flow).

There is a larger space ahead of the LPT stage 1 vanes.

Small gap and larger vanes

Everything is globally continuous, though there is a small gap forward of the LPT stage 1 nozzle which is located in the HPT casing. The vanes themselves are larger axially.

^{CFM56-7B, small gap before LPT Stage 1 vanes}

This location is called the inter-turbine (transition) duct, it corresponds to the interface between HPT and LPT which are rotating at different speeds. The duct has an increasing area due to its "S" shape.

^{Inter-turbine duct geometry. Source}

The gap allows to get a smother change and the adequate duct aspect ratio. The longer duct prevents significant pressure loss before reaching the LPT.

To increase engine performance, manufacturers are trying to decrease the length of the duct but this is difficult due to aerodynamic reasons. Shorter ducts are known as aggressive inter-turbine ducts (AITD). See this paper. A similar duct exists between LPC and HPC.

Bearings

Regarding the possible problem with a bearing or a bearing support in the way, the bearings are really smaller than the stages:

^{CFM56-7B, location of rear bearings}

• The No 4 bearing is within the HP shaft.
• The No 5 outer support is within the oil collector shown above, and the bearing itself is within the its support.

Short answer

This space is part of the inter-turbine duct (ITD), it is required, as well as the larger LPT stage 1 vanes, to maintain a satisfactory aerodynamic flow between HPT and LPT rotating at different speeds (in the ratio of 1:3) and having different diameters.

Shortened ITD are complex to design and known under the name of aggressive ITD.

Details

Taking the CFM56-7B (Boeing 737 NG) as an example. This engine has a single stage HPT and a 4 stage LPT.

Each rotor is preceded by stator (nozzle). The role of the stator vanes is to convert pressure into velocity and turn the flow more perpendicular to the rotor blades surface (this is opposite to the compressor stages where the vanes are downstream of the blades to convert added velocity into pressure and straighten the flow).

There is a larger space ahead of the LPT stage 1 vanes.

Small gap and larger vanes

Everything is globally continuous, though there is a small gap forward of the LPT stage 1 nozzle which is located in the HPT casing. The vanes themselves are larger axially.

^{CFM56-7B, small gap before LPT Stage 1 vanes}

This location is called the inter-turbine (transition) duct, it corresponds to the interface between HPT and LPT which are rotating at different speeds. The duct has an increasing area due to its "S" shape.

^{Inter-turbine duct geometry. Source}

The gap allows to get a smother change and the adequate duct aspect ratio. The longer duct prevents significant pressure loss before reaching the LPT.

To increase engine performance, manufacturers are trying to decrease the length of the duct but this is difficult due to aerodynamic reasons. Shorter ducts are known as aggressive inter-turbine ducts (AITD). See this paper. A similar duct exists between LPC and HPC.

Bearings

Regarding the possible problem with a bearing or a bearing support in the way, the bearings are really smaller than the stages:

^{CFM56-7B, location of rear bearings}

• The No 4 bearing is within the HP shaft.
• The No 5 outer support is within the oil collector shown above, and the bearing itself is within the its support.

Short answer

This space is part of the inter-turbine duct (ITD), it is required, as well as the larger LPT stage 1 vanes, to maintain a satisfactory aerodynamic flow between HPT and LPT rotating at different speeds (in the ratio of 1:3) and having different diameters.

Shortened ITD are complex to design and known under the name of aggressive ITD.

Details

Taking the CFM56-7B (Boeing 737 NG) as an example. This engine has a single stage HPT and a 4 stage LPT.

Each rotor is preceded by stator (nozzle). The role of the stator vanes is to convert pressure into velocity and turn the flow more perpendicular to the rotor blades surface (this is opposite to the compressor stages where the vanes are downstream of the blades to convert added velocity into pressure and straighten the flow).

There is a larger space ahead of the LPT stage 1 vanes.

Small gap and larger vanes

Everything is globally continuous, though there is a small gap forward of the LPT stage 1 nozzle which is located in the HPT casing. The vanes themselves are larger axially.

^{CFM56-7B, small gap before LPT Stage 1 vanes}

This location is called the inter-turbine (transition) duct, it corresponds to the interface between HPT and LPT which are rotating at different speeds. The duct has an increasing area due to its "S" shape.

^{Inter-turbine duct geometry. Source}

The gap allows to get a smother change and the adequate duct aspect ratio. The longer duct prevents significant pressure loss before reaching the LPT.

To increase engine performance, [manufacturers are trying to decrease the length of the duct][4] but this is difficult due to aerodynamic reasons. Shorter ducts are known as aggressive inter-turbine ducts (AITD). See [this paper][5]. A similar duct exists between LPC and HPC.

Bearings

Regarding the possible problem with a bearing or a bearing support in the way, the bearings are really smaller than the stages:

^{CFM56-7B, location of rear bearings}

• The No 4 bearing is within the HP shaft.
• The No 5 outer support is within the oil collector shown above, and the bearing itself is within the its support.