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is the turbo on a diesel engine the same type that is on a unleaded engine?
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The turbocharger doesn't really care what the fuel is as long as the turbine gets hot gasses and the compressor gets cool gasses. A few crazy people have made their own (crude) jet engines based on a salvaged turbocharger.
A turbocharger is an exhaust-driven centrifugal supercharger. Aside from size/capacity of both the turbine and compressor sections, which are generally matched to the size/airflow requirements of the engine the turbo is attached to, they're all basically following the same design configuration.