The invention relates to a rotating mechanical seal arrangement (1) for sealing a product side (5) at a rotating component, comprising a first rotating mechanical seal (2) with a first rotating slide ring (21) and a first stationary slide ring (22) which define a first sealing gap (23) between them, a second rotating mechanical seal (3) with a second rotating slide ring (31) and a second stationary slide ring (32) which define a second sealing gap (33) between them, a fluid space (4) which is limited by the first and second rotating mechanical seals (2, 3), wherein the first rotating mechanical seal (2) is lubricated with a product medium of the product side (5), and wherein the second rotating mechanical seal (3) is lubricated with a liquid quench medium of a quench supply unit (7), the quench medium being located in the fluid space (4), a quench outlet (8) via which quench medium may be discharged from the fluid space (4), a gas outlet (9) via which a gas located in the fluid space may be discharged, and a throttle device (10) which is arranged in the fluid space (4) between the first rotating mechanical seal (2) and the second rotating mechanical seal (3) and divides the fluid space (4) into a product-side fluid space region (4a) and an atmosphere-side fluid space (4b), wherein the gas outlet (9) is arranged at the product-side fluid space region (4a) and the quench outlet (8) is arranged at the atmosphere-side fluid space region (4b).