Turbine heli's
 

This may seem like an odd question, but in the world of turbine helicopters are any turbines designed around the old centripetal design (Frank Whittle) or are they all the newer axial turbine design.

Some have 2 centrifugal compressors, some 6 axial and 1 centrifugal, all depends on how much room there is for the engine, and the designer's country.

As AC says, there is a mixture of designs. Try googling the following models to see more:

General Electric CT-7
Rolls Royce M250 (formerly Allison)
Turbomecca Arriel
Pratt and Whitney PT-6

Thanks chaps

Are you asking about the turboshaft engine's compressor or turbine configuration, or both? Your post asked specifically about "the newer axial turbine design", so I would assume you want to know about the turbine and not the compressor. Regarding the turbine configuration, every modern turboshaft engine I can think of uses axial stages exclusively. I believe the main reason for this is a radial turbine cannot be adequately cooled at the size needed for aircraft turboshaft engine applications.

Regarding compressors, newer turboshaft engines with outputs up to about 3,000 hp use a mix of axial and radial configurations. The radial configuration is preferred for the HP stage(s), since it allows a greater pressure ratio per stage with lower losses. The trend in turboshaft engine design is to push operating pressure ratios higher to improve thermal efficiency, so multiple radial compressor stages are becoming more common.

This was posted on another thread....a Rotorhead Ppruner's excellent teaching aid. You can see the centrifugal stage just aft of the axial compressor stages.

The only modern centrifugal turbine that I can think of is the small industrial Capstone, and maybe some APU's.

Riff, a turbine is by definition "spun" and its function in a jet engine, be it a pure jet or turboshaft, is to further accelerate the exhaust gases in a linear fashion hence its blade geometry is reversed as compared to an axial compressor.
You see how that would make a centrifugal turbine impractical in this example.

tottigol- The more correct term for a radial turbine is "radial inflow turbine". Or sometimes the term "centripetal turbine" is used, which was the specific term used in the OP. Of all the gas turbine devices currently in use, in terms of sheer numbers the radial inflow turbine is by far the most common. This is what every automotive turbocharger uses, and a turbocharger is simply a radial inflow turbine driven by exhaust gas coupled to an intake air radial compressor.

Your point about the suitability of each type of compressor/turbine in regards to local gas flow conditions has merit. One reason aircraft turboshaft engines use axial LP compressors is because they are more tolerant of the variable flow conditions produced in an aircraft intake duct than a radial compressor would be. However, with regards to the turbine exit velocity of the exhaust gas flow, a turboshaft helicopter engine is different than a turboshaft fixed wing engine. A helicopter operates at lower altitudes and at much lower speeds than a fixed wing prop aircraft. So the local airflow conditions (pressure and velocity) at the intake and exhaust are much different. In theory, a radial inflow turbine would work just fine for a helicopter turboshaft engine provided it could handle the thermal and dynamic environment.

Here is a link to a chart that compares the different types of devices for extracting mechanical work from exhaust gas.

At risk of sounding blase...
 

... provided it makes a whirring/shrieking sound when I flick the switch and when I pull that long lever thing up the helicopter goes upward, I'm fairly relaxed about knowing the origins and design terms of an engine I'm using.
Is that wrong?

Though some designs are used in both, of course.....

(PT-6 and CT-7 spring to mind)

Regarding turboshaft engines used in fixed- and rotary-wing applications, in addition to the previously mentioned PT6 and CT7 series, there are also models of the RR 250 and T53 that are used in both. The principal difference is is in the way the propeller and rotor speeds and torque are governed.