A turbomachine combustion chamber fuel supply assembly comprising: - a dual-flow fuel injector intended to inject a primary flow of fuel delivered by a primary fuel supply circuit and a secondary flow of fuel delivered by a secondary fuel supply circuit, - the primary flow of fuel forming a cone of fuel formed by the primary and secondary flows of fuel, - an injection device for injecting the fuel from the injector, the injection device having symmetry of revolution about an axis and comprising, positioned from the upstream to the downstream in the direction in which the flow of fuel flows, a sliding bushing at the center of which the injector is positioned, radial swirl vanes (40, 41, 42) connected by their downstream end to a bowl, the radial swirl vanes (40, 41, 42) comprising a Venturi equipped with an interior wall that has an evolving profile made up of a convergent upstream part connected to a divergent downstream part by a transition region, the Venturi having a minimum inside diameter at the transition region, characterized in that the Venturi has a length, a shape and an axial position which are all designed such that the cone of fuel from the primary circuit strikes the Venturi, the cone of fuel having, downstream of the Venturi, a vertex half-angle β ranging between 30 and 40 degrees, the cone of fuel comprising a central first part and a peripheral second part, the central first part forming a cone with a vertex half-angle α0, this cone being tangential at a point A0 to the downstream divergent part of the Venturi, where α0 is less than β, the peripheral second part forming a cone with a vertex half-angle at the injector outlet ranges between α0 and β, and the cone of fuel, as it leaves the injector, striking the interior wall of the Venturi over a surface extending upstream of the point of tangency A0 as far as a point A1, this point A1 lying upstream of the minimum inside diameter of the Venturi. - a dual-flow fuel injector intended to inject a primary flow of fuel delivered by a primary fuel supply circuit and a secondary flow of fuel delivered by a secondary fuel supply circuit, - the primary flow of fuel forming a cone of fuel formed by the primary and secondary flows of fuel, - an injection device for injecting the fuel from the injector, the injection device having symmetry of revolution about an axis and comprising, positioned from the upstream to the downstream in the direction in which the flow of fuel flows, a sliding bushing at the center of which the injector is positioned, radial swirl vanes (40, 41, 42) connected by their downstream end to a bowl, the radial swirl vanes (40, 41, 42) comprising a Venturi equipped with an interior wall that has an evolving profile made up of a convergent upstream part connected to a divergent downstream part by a transition region, the Venturi having a minimum inside diameter at the transition region, characterized in that the Venturi has a length, a shape and an axial position which are all designed such that the cone of fuel from the primary circuit strikes the Venturi, the cone of fuel having, downstream of the Venturi, a vertex half-angle β ranging between 30 and 40 degrees, the cone of fuel comprising a central first part and a peripheral second part, the central first part forming a cone with a vertex half-angle α0, this cone being tangential at a point A0 to the downstream divergent part of the Venturi, where α0 is less than β, the peripheral second part forming a cone with a vertex half-angle at the injector outlet ranges between α0 and β, and the cone of fuel, as it leaves the injector, striking the interior wall of the Venturi over a surface extending upstream of the point of tangency A0 as far as a point A1, this point A1 lying upstream of the minimum inside diameter of the Venturi.